# Infinity

**Infinity** (∞), quantity greater than any finite quantity. In modern mathematics infinity is viewed in 2 ways. In one, the word has a definite meaning; and with transfinite cardinal numbers, for example, it may have a plurality of meanings. In the other, infinity is seen as a limit: to say that parallel lines intersect at infinity, for example, means merely that the point of intersection of 2 lines may be made to recede indefinitely by making the lines more and more nearly parallel. Similarly, in f(*x*)=1/*x* it is meaningful to say that f(*x*) tends to infinity as *x* tends to zero; again, the sequence 1,2,3,….*n* tends to infinity because, however large *n* is chosen, there is an (*n*+1) greater than it. In advanced set theory an infinite set is defined as one whose elements can be put in a one-to-one correspondence with those of a proper subset of the set (i.e., a subset that is not the whole set).

*See also:* Set theory.

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21st Century Webster's Family Encyclopedia21st Century Webster's Family Encyclopedia - Inert gas to Jaruzelski, Wojciech