Infinity

Georg Cantor makes an appearance as a character, and the hero finds a physical correlate for Cantor's Continuum Problem. The 20th century animosity of Muslim leaders towards Zionism, the political movement of Jewish self-determination, has led to a renewed interest in the relationship between Judaism and Islam. Rudy Rucker's novel White Light describes a mathematician who leaves his body and travels to a kind of afterworld that includes a mountain whose Absolute Infinite height matches that of the class of all ordinals. The period around 900 to 1200 in Moorish Spain came to be known as the Golden age of Jewish culture in Spain. Looking up into the night sky is looking into infinity -- distance is incomprehensible and therefore meaningless.". Under Islamic rule, Judaism has been practiced for almost 1500 years and this has led to an interplay between the two religions which has been positive as well as negative at times. Another quote from The Hitchhiker's Guide to the Galaxy states: "Infinity itself looks flat and uninteresting. If a member of The Church of Jesus Christ of Latter-day Saints has an established Jewish heritage and lineage, then they are considered by the Mormons to be of the Tribe of Judah, and as such, considered both Mormon and Jewish by Mormon authorities.

The Hitchhiker's Guide to the Galaxy contains the following definition of infinity:. These groups are viewed highly negatively by all Jewish denominations, which typically see them as covert and deceptive attempts to convert Jews to Christianity, a view Messianic-Jewish groups strongly contest. Brouwer, David Hilbert, Bertrand Russell, Kurt Gödel and Georg Cantor. These groups have attracted tens (and perhaps hundreds) of thousands of Jews and Christians to their ranks; members identify themselves as Jews. The footnote on p.335 of his book suggests the consideration of the following names: Abraham Robinson, Plato, Thomas Aquinas, L.E.J. Messianic Judaism (sometimes Hebrew Christianity) is the common designation for a number of Christian groups which include varying degrees of Jewish practice. Rudy Rucker, in his book Infinity and the Mind -- the science and philosophy of the mind (1982), has worked out a model list of representatives of each of the eight possible standpoints. Since the Holocaust, there has been much to note in the way of reconciliation between some Christian groups and the Jewish people; the article on Christian-Jewish reconciliation studies this issue.

And in between there are the various possibilities. Though this gain has not offset the general demographic loss due to intermarriage and acculturation, many Jewish communities and movements are growing. There are scientists who hold that all three really exist and there are scientists who hold that none of the three exist. There is a separate article on the Baal teshuva movement, the movement of Jews returning to observant Judaism. Besides the mathematical infinity and the physical infinity, there could also be a philosophical infinity. Complementing the increased popularity of the major denominations has been a number of new approaches to Jewish worship, including feminist approaches to Judaism and Jewish renewal movements. If the universe is indeed ever expanding as science suggests then you could never get back to your starting point even on an infinite time scale. All of the major Jewish denominations have experienced a resurgence in popularity, with increasing numbers of younger Jews participating in Jewish education, joining synagogues, and becoming (to varying degrees) more observant.

The universe, at least in principle, might have a similar topology; if you fly your space ship straight ahead long enough, perhaps you would eventually revisit your starting point. In the last 50 years there has been a general increase in interest in religion among many segments of the Jewish population. By walking/sailing/driving straight long enough, you'll return to the exact spot you started from. This is indicative of the general population trends among the Jewish community in the Diaspora, but a focus on population masks the diversity of current Jewish religious practice, as well as growth trends among some communities, like haredi Jews. The two-dimensional surface of the Earth, for example, is finite, yet has no edge. Due to intermarriage and low birth rates, the Jewish population in the US shrank from 5.5 million in 1990 to 5.1 million in 2001. Note that the question of being infinite is logically separate from the question of having boundaries. Intermarriage rates range from 40-50% in the US, and only about a third of children of intermarried couples are raised Jewish.

An intriguing question is whether actual infinity exists in our physical universe: Are there infinitely many stars? Does the universe have infinite volume? Does space "go on forever"? This is an important open question of cosmology. Dorff, The Rabbinical Assembly, 1996). In quantum field theory infinities arise which need to be interpreted in such a way as to lead to a physically meaningful result, a process called renormalization. 27, Elliot N. Physicists however require that the end result be physically meaningful. (This is My Beloved, This is My Friend: A Rabbinic Letter on Intimate relations, p. For convenience sake, calculations, equations, theories and approximations often use infinite series, unbounded functions, etc., and may involve infinite quantities. Since American Jews are marrying at a later time in their life than they used to, and are having fewer children than they used to, the birth rate for American Jews has dropped from over 2.0 down to 1.7 (the replacement rate is 2.1).

This point of view does not mean that infinity cannot be used in physics. Religious (and secular) Jewish movements in the USA and Canada perceive this as a crisis situation, and have grave concern over rising rates of intermarriage and assimilation in the Jewish community. Likewise, perpetual motion machines theoretically generate infinite energy by attaining 100% efficiency or greater, and emulate every conceivable open system; the impossible problem follows of knowing that the output is actually infinite when the source or mechanism exceeds any known and understood system. Of that population of connected Jews, 80% participated in some sort of Jewish religious observance, but only 48% belonged to a synagogue. There exists the concept of infinite entities (such as an infinite plane wave) but there are no means to generate such things. For example, in the world's largest Jewish community, the United States, according to the 2001 National Jewish Population Survey, 4.3 million out of 5.1 million Jews had some sort of connection to the religion. It is for example presumed impossible for any body to have infinite mass or infinite energy. In most Western nations, such as the United States of America, Israel, Canada, United Kingdom, Argentina and South Africa, a wide variety of Jewish practices exist, along with a growing plurality of secular and non-practicing Jews.

It is therefore assumed by physicists that no measurable quantity could have an infinite value, for instance by taking an infinite value in an extended real number system (see also: hyperreal number), or by requiring the counting of an infinite number of events. A Jewish day of mourning, Yom HaShoah, was inserted into the Jewish calendar commemorating the Holocaust. counting). While the Holocaust, the genocide of millions of Jews under Nazi Germany in World War II, did not directly affect Jewish denominations, the great loss of life it caused resulted in a radical demographic shift, ultimately transforming the makeup of organized Judaism into the way it is today. In physics, approximations of real numbers are used for continuous measurements and natural numbers are used for discrete measurements (i.e. A number of smaller groups came into being as well. The number Infinity plus 1 is also used sometimes in common speech. The thrust and counter-thrust between supporters of Haskalah and more traditional Jewish concepts eventually led to the formation of a number of different branches of Judaism: Haskalah supporters founded Reform Judaism and Liberal Judaism, while traditionalists founded many forms of Orthodox Judaism, and Jews seeking a balance between the two sides founded Conservative Judaism.

These terms describe things that are only potential infinities; it is impossible to play a video game for an infinite period of time or keep a computer running for an infinite period of time. It placed an emphasis on integration with secular society and a pursuit of non-religious knowledge. See halting problem. A parallel Jewish movement, Haskalah or the "Jewish Enlightenment," began, especially in Central Europe, in response to both the Enlightenment and these new freedoms. In practice however, some programming loops considered as infinite will halt by exceeding the (finite) number range of one of its variables. The Enlightenment led to reductions in the European laws that prohibited Jews to interact with the wider secular world, thus allowing Jews access to secular education and experience. In theory, as long as there is no external interaction, the loop will continue to run for all time. In the late 18th century CE Europe was swept by a group of intellectual, social and political movements known as the Enlightenment.

An infinite loop in computer programming is a conditional loop construction whose condition always evaluates to true. Since then all the sects of Hasidic Judaism have been subsumed into mainstream Orthodox Judaism, particularly Haredi Judaism. In video games, infinite lives and infinite ammo refer to a never-ending supply of lives and ammunition. Some of the reasons for the rejection of Hasidic Judaism were the overwhelming exuberance of Hasidic worship; their untraditional ascriptions of infallibility and alleged miracle-working to their leaders, and the concern that it might become a messianic sect. For example, "The movie was infinitely boring, but we had to wait forever to get tickets.". "opponents"). In common parlance, infinity is often used in a hyperbolic sense. European Jews who rejected the Hasidic movement were dubbed by the Hasidim as mitnagdim, (lit.

Leopold Kronecker rejected the notion of infinity and began a school of thought, in the philosophy of mathematics called finitism, which led to the philosophical and mathematical school of mathematical constructivism. Early on, there was a serious schism between Hasidic and non-Hasidic Jews. One example of this is Hilbert's paradox of the Grand Hotel. Waves of Jewish immigration in the 1880s carried it to the United States. Our intuition gained from finite sets breaks down when dealing with infinite sets. Hasidic Judaism eventually became the way of life for many Jews in Europe. Certain extended number systems, such as the hyperreal numbers, incorporate the ordinary (finite) numbers and infinite numbers of different sizes. His disciples attracted many followers; they themselves established numerous Hasidic sects across Europe.

Cantor's views prevailed and modern mathematics accepts actual infinity. It originated in a time of persecution of the Jewish people, when European Jews had turned inward to Talmud study; many felt that most expressions of Jewish life had become too "academic", and that they no longer had any emphasis on spirituality or joy. If a set is too large to be put in one to one correspondence with the positive integers, it is called uncountable. Hasidic Judaism was founded by Israel ben Eliezer (1700-1760), also known as the Ba'al Shem Tov (or Besht). The smallest ordinal infinity is that of the positive integers, and any set which has the cardinality of the integers is countably infinite. With the rise of the Churches, attacks on Jews became motivated instead by theological considerations specifically deriving from Christian views about Jews and Judaism. Cardinal numbers define the size of sets, meaning how many members they contain, and can be standardized by choosing the first ordinal number of a certain size to represent the cardinal number of that size. Ancient repression was politically motivated and Jews were treated no differently than any other ethnic group would have been.

Generalizing finite and the ordinary infinite sequences which are maps from the positive integers leads to mappings from ordinal numbers, and transfinite sequences. This was different in quality to any repressions of Jews in ancient times. Ordinal numbers may be identified with well-ordered sets, or counting carried on to any stopping point, including points after an infinite number have already been counted. Anti-semitism arose during the Middle Ages, in the form of persecutions, pogroms, forced conversion, social restrictions and ghettoization. Cantor defined two kinds of infinite numbers, the ordinal numbers and the cardinal numbers. This split is cultural, and is not based on any doctrinal dispute, although the distance did result in minor differences in practice and prayers. An infinite set can simply be defined as one having the same size as at least one of its "proper" parts; this notion of infinity is called Dedekind infinite. Over time Jews developed into distinct ethnic groups — amongst others, the Ashkenazi Jews (of Central and Eastern Europe with Russia); the Sephardi Jews (of Spain, Portugal, and North Africa) and the Yemenite Jews, from the southern tip of the Arabian peninsula.

Dedekind's approach was essentially to adopt the idea of one-to-one correspondence as a standard for comparing the size of sets, and to reject the view of Galileo (which derived from Euclid) that the whole cannot be the same size as the part. Rabbinical and Karaite Jews each hold that the others are Jews, but that the other faith is erroneous. This modern mathematical conception of the quantitative infinite developed in the late nineteenth century from work by Cantor, Gottlob Frege, Richard Dedekind and others, using the idea of collections, or sets. Karaites exist in small numbers today, mostly living in Israel. Georg Cantor developed a system of transfinite numbers, in which the first transfinite cardinal is aleph-null (), the cardinality of the set of natural numbers. They soon developed oral traditions of their own which differed from the rabbinic traditions, and eventually formed the Karaite sect. A different type of "infinity" are the ordinal and cardinal infinities of set theory. These included the Isunians, the Yudganites, the Malikites, and others.

This is because zero times infinity is undefined. Like the Sadducees who relied only on the Torah, some Jews in the 8th and 9th centuries rejected the authority and divine inspiration of the oral law of the Pharisees/rabbis, as recorded in the Mishnah (and developed by later rabbis in the two Talmuds), relying instead only upon the Tanakh. Notice that . Consequently, a number of other core tenets of the Pharisees' belief system (which became the basis for modern Judaism), were also dismissed by the Sadducees. Infinity is not a real number but may be considered part of the extended real number line, in which arithmetic operations involving infinity may be performed. The Sadducees' rejected the divine inspiration of the Prophets and the Writings, relying only on the Torah as divinely inspired.
. Christianity survived, but by breaking with Judaism and becoming a separate religion; the Pharisees survived but in the form of Rabbinic Judaism (today, known simply as "Judaism").

One important example of such functions is the group of Möbius transformations. After the destruction of the Second Temple in 70 CE, these sects vanished. The domain of a complex-valued function may be extended to include the point at infinity as well. Around the first century CE there were several small Jewish sects: the Pharisees, Sadducees, Zealots, Essenes, and Christians. In this context is often useful to consider meromorphic functions as maps into the Riemann sphere taking the value of at the poles. Following the destruction of Jerusalem and the expulsion of the Jews, Jewish worship stopped being centrally organized around the Temple, and instead was rebuilt around rabbis who acted as teachers and leaders of individual communities (see Jewish diaspora). When this is done, the resulting space is still a one-dimensional complex manifold and called the extended complex plane or the Riemann sphere. Following a second revolt, Jews were not allowed to enter the city of Jerusalem and most Jewish worship was forbidden by Rome.

A point labeled can be added to the complex plane as a topological space giving the one-point compactification of the complex plane. After a Jewish revolt against Roman rule in 66 CE, the Romans all but destroyed Jerusalem; only a single "Western Wall" of the Second Temple remained. means that the magnitude | x | of x grows beyond any assigned value. Among other accomplishments of the Great Assembly, the last books of the Bible were written at this time. As in real analysis, in complex analysis the symbol , called "infinity", denotes an unbounded limit. During the early years of the Second Temple, the highest religious authority was a council known as the Great Assembly, led by Ezra of the Book of Ezra. Infinity is often used not only to define a limit but as if it were a value in the extended real numbers in real analysis; if f(t) ≥ 0 then. A new Second Temple was constructed, and old religious practices were resumed.

Projective geometry also introduces a line at infinity in plane geometry, and so forth for higher dimensions. The Judean elite was exiled to Babylonia, but later at least some of them returned to their homeland after the subsequent conquest of Babylonia by the Persians seventy years later, a period known as the Babylonian Captivity. We can also treat and as the same, leading to the one-point compactification of the real numbers, which is the real projective line. The Kingdom of Judah continued as an independent state until it was conquered by a Babylonian army in the early 6th century BCE, destroying the First Temple that was at the centre of ancient Jewish worship. Adding algebraic properties to this gives us the extended real numbers. The Kingdom of Israel was conquered by the Assyrian ruler Shalmaneser V in the 8th century BCE and spread all over the Assyrian empire, where they were assimilated into other cultures and become known as the Ten Lost Tribes. Points labeled and can be added to the real numbers as a topological space, producing the two-point compactification of the real numbers. After Solomon's reign the nation split into two kingdoms, the Kingdom of Israel (in the north) and the Kingdom of Judah (in the south).

means that x grows beyond any assigned value, and means x is eventually less than any assigned value. A kingdom was established under Saul and continued under King David and Solomon with its capital in Jerusalem. In real analysis, the symbol , called "infinity", denotes an unbounded limit. After the Exodus from Egypt, the Jews came to Canaan, and settled the land. The infinity symbol is represented in Unicode by the character ∞ (∞). Jews trace their religious lineage to the biblical patriarch Abraham through Isaac and Jacob. Another conjecture is that he derived it from the Greek letter ω (omega), the last letter in the Greek alphabet. Jewish history is an extensive topic; this section will cover the elements of Jewish history of most importance to the Jewish religion and the development of Jewish denominations.

One conjecture about why he chose this symbol is that he derived it from a Roman numeral for 1000 that was in turn derived from the Etruscan numeral for 1000, which looked somewhat like CIƆ and was sometimes used to mean "many". However, in most Orthodox synagogues these positions are filled by laypeople. John Wallis is usually credited with introducing ∞ as a symbol for infinity in 1655 in his De sectionibus conicus. Since the Enlightenment large synagogues have often adopted the practice of hiring rabbis and hazzans to act as shatz and baal koreh, and this is still typically the case in most Conservative and Reform congregations. However, this explanation is improbable, since the symbol had been in use to represent infinity for over two hundred years before August Ferdinand Möbius and Johann Benedict Listing discovered the Möbius strip in 1858. The three preceding positions are usually voluntary and considered an honor. Again, one can imagine walking along its surface forever. Many congregations, especially larger ones, also rely on a:.

A popular explanation is that the infinity symbol is derived from the shape of a Möbius strip. Often there are several people capable of filling these roles and different services (or parts of services) will be led by each. One can imagine walking forever along a simple loop formed from a ribbon. The same person is often qualified to fill more than one role, and often does. One possibility is suggested by the name it is sometimes called — the lemniscate, from the Latin lemniscus, meaning "ribbon". Note that these roles are not mutually exclusive. The precise origins of the infinity symbol ∞ are unclear. Jewish prayer services do involve two specified roles, which are sometimes, but not always, filled by a rabbi and/or hazzan in many congregations:.

Unlike the traditional empiricists, he thought that the infinite was in some way given to sense experience. The most common professional clergy in a synagogue are:. An exception was Wittgenstein, who made an impassioned attack upon axiomatic set theory, and upon the idea of the actual infinite, during his "middle period".². Some activities -- reading the Torah and haftarah (a supplementary portion from the Prophets or Writings); the prayer for mourners; the blessings for bridegroom and bride; the complete grace after meals -- require a minyan, the presence of ten adults (Orthodox Jews and some Conservative Jews require ten adult men; some Conservative Jews and Reform Jews include women in the minyan). Modern discussion of the infinite is now regarded as part of set theory and mathematics, and generally avoided by philosophers. A Jew can fulfil most requirements for prayer by himself. A potential infinity is allowed by letting an infinitely-large quantity be cancelled out by an infinitely-small quantity. From the times of the Mishna and Talmud to the present, Judaism has required specialists or authorities for the practice of very few rituals or ceremonies.

Potentiality lies in the definitions of this operation, as well-defined and interconsistent mathematical axioms. The priesthood is an inherited position, and although priests no longer have clerical duties, they are still honored in many Jewish communities. Such seeming paradoxes are resolved by taking any finite figure and stretching its content infinitely in one direction; the magnitude of its content is unchanged as its divisions drop off geometrically but the magnitude of its bounds increases to infinity by necessity. Technically, the last time Judaism had a clergy was prior to the destruction of the Second Temple in 70 CE, when priests attended to the Temple and sacrifices. Not reported, this motivation of Hobbes came too late as curves having infinite length yet bounding finite areas were known much before. Judaism does not have a clergy, in the sense of full-time specialists required for religious services. Famously, the ultra-empiricist Hobbes tried to defend the idea of a potential infinity in the light of the discovery by Evangelista Torricelli, of a figure (Gabriel's horn) whose surface area is infinite, but whose volume is finite. Life-cycle events occur throughout a Jew's life that bind him/her to the entire community.

Our idea of infinity is merely negative or privative. The laws of niddah dictate that sexual intercourse cannot take place while the woman is having a menstrual flow, and she has to count seven "clean" days and immerse in a mikvah (ritual bath) following menstruation. They believed all our ideas were derived from sense data or "impressions", and since all sensory impressions are inherently finite, so too are our thoughts and ideas. The laws of niddah ("menstruant", often referred to euphemistically as "family purity") and various other laws regulating the interaction between men and women (e.g., tzeniut, modesty in dress) are perceived, especially by Orthodox Jews, as vital factors in Jewish life, though they are rarely followed by Reform or Conservative Jews. Locke, in common with most of the empiricist philosophers, also believed that we can have no proper idea of the infinite. Although sometimes rationalized by reference to hygiene, its stated purpose is perhaps better understood as providing certainty that food eaten is prepared and partaken only from sources which are confirmed to have been spiritually appropriate and which avoided spiritual "negatives" such as pain, sickness, unclean animals or abusive practices in its preparation. The idea that size can be measured by one-to-one correspondence is today known as Hume's principle, although Hume, like Galileo, believed the principle could not be applied to infinite sets. Also, mixing meat and milk is not allowed, as this is viewed as cooking the child in its mother's milk.

He thought this was one of the difficulties which arise when we try, "with our finite minds", to comprehend the infinite. Kashrut involves the abstention from consuming animals that eat other animals, and that roam the sea floor eating the excretions of other animals, therefore excluding birds/beasts of prey and seafood (other than fish), respectively. It appeared, by this reasoning, as though a set which is naturally smaller than the set of which it is a part (since it does not contain all the members of that set) is in some sense the same size. From the context of the laws in the book of Leviticus, the purpose of kashrut is related to ritual purity and holiness, as well as health. For example, we can match up the "set" of even numbers {2, 4, 6, 8 ...} with the natural numbers {1, 2, 3, 4 ...} as follows:. Food in accord with Jewish law is termed kosher, and food not in accord with Jewish law is termed treifah or treif. Galileo (during his long house arrest in Siena after his condemnation by the Inquisition) was the first to notice that we can place an infinite set into one-to-one correspondence with one of its proper subsets (any part of the set, that is not the whole). The laws of kashrut ("keeping kosher") are the Jewish dietary laws.

Aquinas also argued against the idea that infinity could be in any sense complete, or a totality. In addition to synagogues, other buildings of signficance in Judaism include yeshivas, or institutions of Jewish learning, and mikvahs, which are ritual baths. However, on this view, no infinite magnitude can have a number, for whatever number we can imagine, there is always a larger one: "There are not so many (in number) that there are no more". There is no set blueprint for synagogues and the architectural shapes and interior designs of synagogues vary greatly, so a synagogue may contain any (or none) of these features:. The parts are actually there, in some sense. Synagogues are a Jewish houses of prayer and study, they usually contain separate rooms for prayer (the main sanctuary), smaller rooms for study, and often an area for community or educational use. The second view is found in a clearer form by medieval writers such as William of Ockham:. During the course of a year, the full Torah is read, and the cycle begins again every autumn during Simhat Torah (“rejoicing in the Torah”).

For example, ∀n∈Z(∃m∈Z[m>n∧P(m)]), which reads, "for any integer n, there exists an integer m > n such that P(m)". The core of festival and Sabbath prayer services is the public reading of the Torah, along with connected readings from the other books of the Jewish Bible, called Haftarah. The other is that we may quantify over infinite sets without restriction. There are many minor holidays as well, including Purim, which celebrates the events told in the Biblical book of Esther, and Hanukkah, which is not established in the Bible but which celebrates the successful rebellion by the Maccabees against the Seleucid Empire. One is that it is always possible to find a number of things that surpasses any given number, even if there are not actually such things. Yamim Noraim (Days of Awe or High Holidays) celebrate judgement and forgiveness. This is often called potential infinity; however there are two ideas mixed up with this. They are also pilgrimage holidays, for which the Children of Israel would journey to Jerusalem to offer sacrifices to God in His Temple.

In Europe, the traditional view derives from Aristotle:. They are also timed to coincide with important agricultural seasons. [1] [2] The concept of different orders of infinity would remain unknown in Europe until the late 19th century. Haggim (festivals) celebrate revelation by commemorating different events in the passage of the Children of Israel out of slavery in Egypt to their return to the land of Canaan. It recognises five different types of infinity: infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually. Driving is traditionally forbidden, so many Jews walk to synagogue to participate in Shabbat services. 400 BC) classifies all numbers into three sets: enumerable, innumerable and infinite. For example, writing, carrying items in public, and lighting fires are considered to be work.

The Indian Jaina mathematical text Surya Prajinapti (ca. During Shabbat, Jews are forbidden to engage in any activity that falls under 39 categories of work. The earliest known documented knowledge of infinity is presented in the Veda- Yajur Veda which states that "if you remove a part from infinity or add a part to infinity, still what remains is infinity". The evening meal begins with a sanctification of Shabbat made over a cup of wine, and a blessing said over two loaves of bread. . At the beginning of Shabbat, it is usual for the woman of the house to light a pair of candles and say a blessing praising God. For a discussion about infinity and the physical universe, see Universe. It plays an important role in Jewish practice and is the subject of a large body of religious law.

In popular culture, we have Buzz Lightyear's rallying cry, "To infinity — and beyond!", which may also be viewed as the rallying cry of set theorists considering large cardinals.¹. Shabbat, the weekly day of rest lasting from shortly before sundown on Friday night to shortly after sundown Saturday night, commemorates God's day of rest upon the completion of creation as well as the Exodus from Egypt. By some, infinity is considered to be not a number but a concept of increase beyond bounds. Jewish holy days celebrate central themes in the relationship between God and the world, such as creation, revelation, and redemption. In mathematics, infinity is relevant to, or the subject matter of, articles such as mathematical limits, aleph numbers, classes in set theory, Dedekind-infinite sets, large cardinals, Russell's paradox, hyperreal numbers, projective geometry, extended real numbers and the Absolute Infinite. While all use the same set of prayers and texts, the frequency of prayer, the number of prayers recited at various religious events, and whether one prays in a particular liturgical language or the vernacular differs from denomination to denomination, with Conservative and Orthodox congregations using more traditional services, and Reform and Reconstructionist synagogues more likely to incorporate translations, contemporary writings, and abbreviated services. In both theology and philosophy, infinity is explored in articles such as the Ultimate, the Absolute, God, and Zeno's paradoxes. The Jewish approach to prayer differs among the various branches of Judaism.

In philosophy, infinity can be attributed to space and time, as for instance in Kant's first antinomy. Phylacteries or tefillin, boxes containing the portions of the Torah mandating them, are also worn by religious Jews during weekday morning services. In theology, for example in the work of theologians such as Duns Scotus, the infinite nature of God invokes a sense of being without constraint, rather than a sense of being unlimited in quantity. A kippah or yarmulke--pronounced ya-ma-ka (skullcap) is a head covering worn during prayer by most Jews, and at all times by more orthodox Jews — especially Ashkenazim. The word infinity comes from the Latin infinitas, "unboundedness". The tallit is a Jewish prayer shawl. Popular or colloquial usage of the term often does not accord with its more technical meanings. There are a number of common Jewish religious objects used in prayer.

Infinity refers to several distinct concepts which arise in theology, philosophy, mathematics and everyday life. There are also prayers and benedictions recited throughout the day, such as those before eating (The Hamotzi) or drinking (Kiddush). and . This is called a minyan (prayer quorum). and . However, in order to have an actual service, you are required to have ten people. If then and . The shema states, "Shema Yisrael Adonai Eloheinu Adonai Echad," or "Hear O Israel, the Lord is our God, the Lord is One." Most of the prayers in a traditional Jewish service can be said in solitary prayer.

If then and . Another key prayer in many services is the declaration of faith, the Shema which is recited at shacharit and maariv. and . All services include a number of benedictions called the Amidah or the Shemonah Esrei ("eighteen"), which on weekdays consists of nineteen blessings (one was added in the time of the Mishna, but the name remains). and . There are three main daily prayer services, named Shacharit, Mincha (literally: "flour-offering") and Maariv or Arvit. means that the area under f(t) approaches 1. The main article Jewish views of religious pluralism describes how Judaism views other religions; it also describes how members of each of the Jewish religious denominations view the other denominations.

means that the area under f(t) is not finite. In other areas, such as Greece, the Nazis deemed Karaites as belonging to a greater Jewish tradition and abused them accordingly. means that f(t) does not bound a finite area from 0 to 1. It is interesting to note that the Nazis often did not associate Karaites with Jews, and therefore several Karaite communities were spared in WWII and exist to this day even in places such as Lithuania where Jewish communities were completely devastated. Some European Karaites do not see themselves as part of the Jewish community, while most do. The Karaites, or "Scripturalists," accept only the Hebrew Bible and what they view as the Peshat: "Plain or Simple Meaning"; and do not accept non-biblical writings as authoritative.

The followers of Karaism believe they are the remnants of the non-Rabbinic Jewish sects of the Second Temple period, such as the Saducees, though others contend they are a sect started in the 8th and 9th centuries. Unlike the above denominations, which were ideological reactions that resulted from the exposure of traditional rabbinic Judaism to the radical changes of modern times, Karaite Judaism did not begin as a modern Jewish movement. The third group is the largest, and has been the most politically active since the early 1990s. Haredi applies to a populace that can be roughly divided into three separate groups along both ethnic and ideological lines: (1) "Lithuanian" (non-hasidic) haredim of Ashkenazic origin; (2) Hasidic haredim of Ashkenazic origin; and (3) Sephardic haredim.

The former term includes what is called "Religious Zionism" or the "National Religious" community, as well as what has become known over the past decade or so as haredi-leumi (nationalist haredi), or "Hardal," which combines a largely haredi lifestyle with nationalist ideology. What would be called "Orthodox" in the diaspora includes what is commonly called dati (religious) or haredi (ultra-Orthodox) in Israel. Various ways of measuring this percentage, each with its pros and cons, include the proportion of religiously observant Knesset members, the proportion of Jewish children enrolled in religious schools, and statistical studies on "identity". The "Orthodox" spectrum in Israel is a far greater percentage of the Jewish population in Israel than in the diaspora, though how much greater is hotly debated.

Nevertheless, the spectrum covered by "Orthodox" in the diaspora exists in Israel, again with some important variations. The term "Orthodox" (Ortodoxi) is unpopular in Israeli discourse (among both "secular" and "religious" alike). They often overlap, and they cover an extremely wide range in terms of ideology and religious observance. There is a great deal of ambiguity in the ways "secular" and "traditional" are used in Israel.

This term, as commonly used, has nothing to do with the official Masorti (Conservative) movement. The term "traditional" (masorti) is most common as a self-description among Israeli families of "eastern" origin (i.e., the Middle East, Central Asia, and North Africa). This portion of the population largely ignores organized religious life, be it of the official Israeli rabbinate (Orthodox) or of the liberal movements common to diaspora Judaism (Reform, Conservative). The term "secular" is more popular as a self-description among Israeli families of western (European) origin, whose Jewish identity may be a very powerful force in their lives, but who see it as largely independent of traditional religious belief and practice.

Most Jewish Israelis classify themselves as "secular" (hiloni), "traditional" (masorti), "religious" (dati) or Haredi. Even though all of these denominations exist in Israel, Israelis tend to classify Jewish identity in ways that are different than diaspora Jewry. Any Jew who keeps at least those laws would be considered observant and religious. According to most Orthodox Jews, Jewish people who do not keep the laws of Shabbat and Yom Tov (the holidays), Kashrut, and family purity are considered non-religious.

Many religious Jews do not look at one's denomination as a valid way of designating Jews; instead they view Jews by the level of their religious observance. The article on Relationships between Jewish religious movements discusses how different Jewish denominations view each other. For example, it would not be unusual for a Conservative Jew to attend either an Orthodox or Reform synagogue. Nonetheless, there is some level of Jewish unity.

To some degree, these doctrinal differences have created schisms between the Jewish denominations. Over the past two centuries the Jewish community has divided into a number of Jewish denominations; each has a different understanding of what principles of belief a Jew should hold, and how one should live as a Jew. Major changes occurred in response to the Enlightenment (late 1700s to early 1800s) leading to the post-Enlightenment Jewish philosophers, and then modern Jewish philosophers such as Martin Buber, Franz Rosenzweig, Mordecai Kaplan, Abraham Joshua Heschel, Will Herberg, Emmanuel Levinas, Richard Rubenstein, Emil Fackenheim, and Joseph Soloveitchik. Major Jewish philosophers include Solomon ibn Gabirol, Saadia Gaon, Maimonides, and Gersonides.

Jewish philosophy refers to the conjunction between serious study of philosophy and Jewish theology. The question is far from settled and occasionally resurfaces in Israeli politics. The question of what determines Jewish identity was given new impetus when, in the 1950s, David ben Gurion requested opinions on mihu Yehudi ("who is a Jew") from Jewish religious authorities and intellectuals worldwide. In the past, family and friends were said often to formally mourn for the person, though this is rarely done today.

However, in the latter case, the person loses standing as a member of the Jewish community and becomes known as an apostate. A Jew who ceases to practice Judaism is still considered a Jew, as is a Jew who does not accept Jewish principles of faith and becomes an agnostic or an atheist; so too with a Jew who converts to another religion. (Recently, the American Reform and Reconstructionist movements have included those born of Jewish fathers and gentile mothers, if the children are raised practicing Judaism only.) All mainstream forms of Judaism today are open to sincere converts. According to Jewish law, someone is considered to be a Jew if he or she was born of a Jewish mother or converted in accord with Jewish Law.

The literature of questions to rabbis, and their considered answers, is referred to as responsa (in Hebrew, Sheelot U-Teshuvot.) Over time, as practices develop, codes of Jewish law are written that are based on the responsa; the most important code, the Shulkhan Arukh, largely determines Jewish religious practice up to today. The Halakha has developed slowly, through a precedent-based system. Halakha, the rabbinic Jewish way of life, then, is based on a combined reading of the Torah, and the oral tradition - the Mishnah, the halakhic Midrash, the Talmud and its commentaries. These have been expounded by commentaries of various Torah scholars during the ages.

Over the next four centuries this law underwent discussion and debate in both of the world's major Jewish communities (in Israel and Babylonia), and the commentaries on the Mishnah from each of these communities eventually came to be edited together into compilations known as the two Talmuds. By the time of Rabbi Judah Ha-Nasi (200 CE), after the destruction of Jerusalem, much of this material was edited together into the Mishnah. This parallel set of material was originally transmitted orally, and came to be known as "the oral law". To justify this viewpoint, Jews point to the text of the Torah, where many words are left undefined, and many procedures mentioned without explanation or instructions; this, they argue, means that the reader is assumed to be familiar with the details from other, i.e., oral, sources.

Rabbinic Judaism has always held that the books of the Tanakh (called the written law) have always been transmitted in parallel with an oral tradition. These oral traditions were transmitted by the Pharisee sect of ancient Judaism, and were later recorded in written form and expanded upon by the rabbis. While there have been Jewish groups which claimed to be based on the written text of the Torah alone (e.g., the Sadducees, and the Karaites), most Jews believed in what they call the oral law. Many laws were only applicable when the Temple in Jerusalem existed, and fewer than 300 of these commandments are still applicable today.

Some of these laws are directed only to men or to women, some only to the ancient priestly groups, the Kohanim and Leviyim (members of the tribe of Levi), some only to those who practice farming within the land of Israel. According to rabbinic tradition there are 613 commandments in the Torah. The basis of Jewish law and tradition ("halakha") is the Torah (the five books of Moses). Related Topics.

For more detail, see Rabbinic literature. The following is a basic, structured list of the central works of Jewish practice and thought. Jews are often called a "People of the Book," and Judaism has an age-old intellectual tradition focusing on text-based Torah study. Of these, the one most widely considered authoritative is Maimonides' thirteen principles of faith:.

Over the centuries, a number of clear formulations of Jewish principles of faith have appeared, many with common elements, and though they differ with respect to certain details, they demonstrate a wide variety of tolerance for varying theological perspectives. Notably, in Orthodox Judaism some principles of faith (e.g., the Divine origin of the Torah) are considered important enough that public rejection of them can put one in the category of "apikoros" (heretic). In attempting to define who is a Jew, the ancient historian Josephus emphasized practices and traditions rather than religious beliefs, associating apostasy with a failure to observe traditional customs, and suggesting the requirements for conversion to Judaism included circumcision and adherence to traditional customs. While individual rabbis, congregations, or movements have at times agreed upon a firm dogma, generally other rabbis and groups have disagreed, and because there is explicitly no central religious authority, no specific formulation of Jewish principles of faith could take precedence over any other.

While Judaism has always affirmed a number of Jewish principles of faith, no creed, dogma, set of orthodox beliefs, or fully-binding "catechism," is recognized, an approach to religious doctrine that dates back at least two thousand years and that makes generalizations about Jewish theology somewhat difficult. In contrast to the Orthodox religious view of the Hebrew Bible, critical biblical scholars also suggest that the Torah consists of a variety of inconsistent texts that were edited together in a way that calls attention to divergent accounts (see Documentary hypothesis). The supposed result is a set of beliefs and practices concerning identity, ethics, and the relationships between man and nature and man and God that examine and privilege "differences" — for example the difference between Jews and non-Jews; the local differences in the practice of Judaism; a close attention, when interpreting texts, to difference in the meanings of three words; attempts to preserve and encode different points of view within texts, and a relative avoidance of creed and dogma. According to this theory, Jews began to grapple with the tension between their claims of particularism (that only Jews were required to obey the Torah), and universalism (that the Torah contained universal truths).

New evidence supporting the existence of a polytheistic precursor to Judaism was unearthed in the discovery of Ugarit, where ancient tablets were found that describe a pantheon of gods that includes several gods mentioned in the Torah. They posit that this attitude reflected a growing Gentile interest in Judaism (some Greeks and Romans considered the Jews a most "philosophical" people because of their belief in a God that cannot be represented visually), and growing Jewish interest in Greek philosophy, which sought to establish universal truths, thus leading - potentially - to the idea of monotheism, at least in the sense that "all gods are One". According to them, it was only by the Hellenic period that most Jews came to believe that their God was the only God (and thus, the God of everyone), and that the record of His revelation (the Torah) contained within it universal truths. Although monotheism is fundamental to Rabbinic Judaism, many critical Bible scholars claim that certain verses in the Torah imply that the early Israelites accepted the existence of other gods, while viewing their God as the sole Creator, whose worship is obligated (a rather henotheistic point of view).

However as the persecutions of the Jews increased and the details were in danger of being forgotten, rabbinic tradition holds that these oral laws were recorded in the Mishnah, and the Talmud, as well as other holy books. The details and interpretation of the law, which are called the Oral Torah or oral law were originally unwritten. Together with the books of the prophets it is called the Written Torah. The Torah given on Mount Sinai was summarized in the five books of Moses.

The Jewish temple is to remain in ruins until a descendant of David arises to restore the glory of Israel and rebuild the Temple in Jerusalem. The Second Temple stood for 420 years, after which it was destroyed by the Roman general (later emperor) Titus. After seventy years the Jews were allowed back into Israel under the leadership of Ezra, and the Temple was rebuilt, as recorded in the Book of Ezra and the Book of Nehemiah. These events are recorded in the Book of Isaiah and the Book of Jeremiah.

The southern Kingdom of Judah, whose capital was Jerusalem, home of the Temple, remained under the rulership of the House of David, however, as in the north, idolatry increased to the point that God allowed Babylonia to conquer the Kingdom, destroy the Temple which had stood for 410 years, and exile its people to Babylonia, with the promise that they would be redeemed after seventy years. After several hundred years, because of rampant idolatry, God allowed Assyria to conquer Israel and exile its people. After Solomon's death, his Kingdom was split into the two kingdoms of Israel and Judah. As a result, it was David's son Solomon who built the first permanent temple according to God's will, in Jerusalem, as described in the Books of Kings.

Once King David was established, he told the prophet Nathan that he would like to build a permanent temple, and as a reward for his actions, God promised David that he would allow his son to build the temple and the throne would never depart from his children (David himself was not allowed to build the temple because he had been involved in many wars, making it inappropriate for him to build a temple representing peace). When the people pressured Saul into going against a command conveyed to him by Samuel, God told Samuel to appoint David in his stead. Samuel grudgingly acceded to this request and appointed Saul, a great but very humble man, to be their King. The people of Israel then told Samuel the prophet that they had reached the point where they needed to be governed by a permanent king, as were other nations, as described in the Books of Samuel.

As time went on, the spiritual level of the nation declined to the point that God allowed the Philistines to capture the tabernacle in Shiloh. This is described in the Book of Joshua and the Book of Judges. Once the Jews had settled in the land of Israel, the tabernacle was planted in the city of Shiloh for over 300 years during which time God provided great men, and occasionally women, to rally the nation against attacking enemies, some of which were sent by God as a punishment for the sins of the people. They first officiated in the tabernacle (a portable house of worship), and later their descendants were in charge of worship in the Temple in Jerusalem.

God designated the descendants of Aaron, Moses' brother, to be a priestly class within the Israelite community. Then God sent Moses to redeem the Israelites from slavery, and after the Exodus from Egypt, God led the Jews to Mount Sinai and gave them the Torah, eventually bringing them to the land of Israel. God sent the patriarch Jacob and his children to Egypt, where after many generations they became enslaved. As a result, God promised he would have children: "Look now toward heaven and count the stars/So shall be your progeny." (Genesis 15:5) Abraham's first child was Ishmael and his second son was Isaac, whom God said would continue Abraham's work and inherit the Land of Israel (then called Canaan), after having been exiled and redeemed.

Rabbinic literature records that he was the first to reject idolatry and preach monotheism. According to Orthodox Judaism and most religious Jews, the Biblical patriarch Abraham was the first Hebrew. This relationship is generally portrayed as contentious, as Jews struggle between their faith in God and their attraction for other gods, and as some Jews, such as Abraham; (most notably and directly), Jacob -- later known as Israel; and Moses struggle with God. 350 BCE).

The subject of the Hebrew Bible is an account of the Israelites' (also called Hebrews) relationship with God as reflected in their history from the beginning of time until the building of the Second Temple (ca. Judaism maintains that this is how the individual will merit rewards in the afterlife, called gan eden (Hebrew: "Garden of Eden") or olam haba ("World to Come"), though Judaism does not have a single concept of the afterlife, nor is the afterlife the focus of Jewish practice. As a matter of practical worship (in comparison to other religions) Judaism seeks to elevate everyday life to the level of the ancient Temple's worship by worshipping God through the spectrum of daily activities and actions. The Children of Israel similarly had a Temple in Jerusalem, a caste of priests, and made sacrifices — but these were not the sole means of worshipping God.

Other religions at the time were characterized by temples in which priests would worship their gods through sacrifice. The Torah (i.e., The Hebrew Bible) specifies a number of laws, known as the 613 mitzvot, to be followed by the Children of Israel. In Judaism, God is unlimited, fully capable, and fully available to care for Creation. The significance of the idea is that an omniscient and omnipotent God created humankind as recorded in the Book of Genesis, in the Creation according to Genesis starting with the very first verse of Genesis 1:1: "In the beginning God created the heavens and the earth," a marked contrast with polytheistic religions in which the gods are limited by their preoccupation with personal desires irrelevant to humankind, by their limited powers, or by the interference of other powers.

(See Ten Commandments: Jewish interpretation). One must not bow down to or serve any being or object but God. It is also a prohibition against making or possessing objects that one may bow down to or serve, such as crucifixes or icons, and any forms of paintings or artistic representations of God. To deny the uniqueness of God is to deny all that is written in the Torah:.

The idea of God as a duality or trinity is heretical for Jews to hold; it is considered akin to polytheism. This prohibits belief in or worship of any additional deities, gods, spirits or incarnations. Furthermore, one is required to believe in God and God alone. To turn from these beliefs is to deny God and the essence of Judaism, according to the Jewish understanding of the Ten Commandments.

Thus the beliefs in the existence of God, God's eternal nature, God as the sole creator of all that exists, and God's determination of the course of events in this world, are the foundations of the Judaistic religion:. Orthodox Judaism claims that it is expressed directly in Torah (the Hebrew Bible), where God incorporates it into the Ten Commandments:. Scholars argue as to when the notion of monotheism arose. The Children of Israel similarly had a Temple in Jerusalem, priests, and made sacrifices -— but these were not the sole means of worshiping God.

Other religions at the time were characterized by temples in which priests would worship their gods through sacrifice. Second, the Torah specifies a number of commandments to be followed by the Children of Israel. In polytheistic religions, humankind is often created by accident, and the gods are primarily concerned with their relations with other gods, not with people. The significance of this idea, according to critical historian Yehezkal Kaufman, lies in that Judaism holds that God created, and cares about, humankind.

One characteristic was monotheism. According to both traditional Judaism and modern scholars, a number of qualities distinguish Judaism from the other religions that existed when it first emerged. . Thus, Talmud professor Daniel Boyarin has argued that "Jewishness disrupts the very categories of identity, because it is not national, not genealogical, not religious, but all of these, in dialectical tension."



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During this time, Jews have experienced slavery, anarchic and theocratic self-government, conquest, occupation, and exile; they have been in contact with, and have been influenced by, ancient Egyptian, Babylonian, Persian, and Hellenic cultures, as well as modern movements such as the Enlightenment (see Haskalah) and the rise of nationalism. Judaism does not fit easily into conventional Western categories, such as religion, ethnicity, or culture, in part because of its 4,000-year history. The practice of Judaism is devoted to the study and observance of these laws and commandments, as they are interpreted according to the Tanakh, Halakha, responsa and rabbinic literature. According to Jewish thought, the God who created the world established a covenant with the Jewish people, and revealed his laws and commandments to them in the form of the Torah.

Despite this, Judaism in all its variations has remained tightly bound to a number of religious principles, the most important of which is the belief in a single, omniscient, omnipotent, omnibenevolent, transcendent God, who created the universe and continues to be involved in its governance. Over at least the last two thousand years, Judaism has not been monolithic in practice, and has not had any centralized authority or binding dogma. The tenets and history of Judaism are the major part of the foundation of other Abrahamic religions, including Samaritanism, Christianity, and Islam. It is one of the first recorded monotheistic faiths and one of the oldest religious traditions still practiced today.

Judaism is the religion of the Jewish people, with around 14 million followers (as of 2005 [1]). Either an expert in the laws of kashrut, or (generally) under the supervision of a rabbi who is expert in those laws. Mashgiach over kosher products - supervises merchants and manufacturers of kosher food to ensure that the food is kosher. Oversees the emotional and spiritual welfare of the students in a yeshiva, and gives lectures on mussar.

Mashgiach of a yeshiva - expert in mussar (ethics). Somebody who is an expert in delving into the depths of the Talmud, and lectures the highest class in a yeshiva. Rosh yeshivah - head of a yeshiva. Sofer (scribe) - Torah scrolls, tefillin (phylacteries), mezuzot (scrolls put on doorposts), and gittin (bills of divorce) must be written by a sofer who is an expert in the laws of writing.

In order for meat to be kosher, it must be slaughtered by a shochet who is expert in the laws and has received training from another shochet, as well as having regular contact with a rabbi and revising the relevant guidelines on a regular basis. Shochet (ritual slaughterer) - slaughters all kosher meat. An expert in the laws of circumcision who has received training from a qualified mohel. Mohel - performs the brit milah (circumcision).

A dayan always requires semicha. Dayan (judge) - expert in Jewish law who sits on a beth din (rabbinical court) for either monetary matters or for overseeing the giving of a bill of divorce (get). Gabbai (sexton) - Calls people up to the Torah, appoints the shatz for each prayer session if there is no standard shatz, and makes certain that the synagogue is kept clean and supplied. The requirements for acting as baal koreh are the same as those for the shatz.

Baal koreh (master of the reading) reads the weekly Torah portion. Any adult capable of speaking Hebrew clearly may act as shatz (Orthodox Jews and some Conservative Jews allow only men to act as shatz; some Conservative Jews and Reform Jews allow women to act as shatz as well). The entire congregation participates in the recital of such prayers by saying amen at their conclusion; it is with this act that the shatz's prayer becomes the prayer of the congregation. When a shatz recites a prayer on behalf of the congregation, he is not acting as an intermediary but rather as a facilitator.

Shaliach tzibur or Shatz (leader -- literally "agent" or "representative" -- of the congregation) leads those assembled in prayer, and sometimes prays on behalf of the community. A congregation does not need to have a dedicated hazzan. Chosen for a good voice, knowledge of traditional tunes, understanding of the meaning of the prayers and sincerity in reciting them. Chazzan (note: the "ch" denotes voiceless pharyngeal fricative) (cantor) - a trained vocalist who acts as shatz.

Hassidic Rebbe - rabbi who is the head of a Hassidic dynasty. Some congregations have a rabbi but also allow members of the congregation to act as shatz or baal koreh (see below).