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.