infinitely

1. Having no boundaries or limits.

2. Immeasurably great or large; boundless: infinite patience; a discovery of infinite importance.

3. Mathematics

   1. Existing beyond or being greater than any arbitrarily large value.

   2. Unlimited in spatial extent: a line of infinite length.

   3. Of or relating to a set capable of being put into one-to-one correspondence with a proper subset of itself.

Synonyms: These adjectives mean being without beginning or end: infinite wisdom; boundless ambition; eternal beauty; illimitable space; sempiternal truth. See Also Synonyms at incalculable.

Usage Note: Infinite is sometimes grouped with absolute terms such as unique, absolute, and omnipotent, since in its strict mathematical sense infiniteness is an absolute property; some infinite sets are smaller than others, but they are no less infinite. In nontechnical usage, of course, infinite is often used to refer to an unimaginably large degree or amount, and in these cases it is acceptable to modify or compare the word: Nothing could give me more infinite pleasure than to see you win. Withdrawing the troops would create an even more infinite set of problems for the coalition. · Note that unlike other incomparable adjectives, infinite when used in its strict literal sense cannot be modified by words like nearly, since quantities do not approach infinity by degrees. This constraint, too, can be ignored when the word is used simply to refer to a very large number: You need a nearly infinite amount of patience to do the job. See Usage Notes at absolute, unique.

1. Relating to a set that can be put into a one-to-one correspondence with some proper subset of its own members.

2. Relating to or being a numerical quantity describing the size of such a set.

3. Being without an upper or lower numerical bound.