In mathematics, especially in set theory, when dealing with sets of infinite size, the term almost or nearly is used to mean all the elements except for finitely many. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has media related to: Mathematics Inter. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ...

In other words, an infinite set S that is a subset of another infinite set L, is almost L if the subtracted set LS is of finite size. A is a subset of B, and B is a superset of A. In mathematics, especially in set theory, a set A is a subset of a set B, if A is contained inside B. Every set is a subset of itself. ...

Examples:

• The set is almost N for any k in N, because only finitely many natural numbers are less than k.
• The set of prime numbers is not almost N because there are infinitely many natural numbers that are not prime numbers.

This is conceptually similar to the almost everywhere concept of measure theory, but is not the same. For example, the Cantor set is uncountably infinite, but has Lebesgue measure zero. So a real number in (0, 1) is a member of the complement of the Cantor set almost everywhere, but it is not true that the complement of the Cantor set is almost the real numbers in (0, 1). Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), and they can be used for ordering (this is... In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. ... In measure theory (a branch of mathematical analysis), one says that a property holds almost everywhere if the set of elements for which the property does not hold is a null set, i. ... In mathematics, a measure is a function that assigns a number, e. ... The Cantor set, introduced by German mathematician Georg Cantor, is a remarkable construction involving only the real numbers between zero and one. ... In mathematics, an uncountable set is a set which is not countable. ... In mathematics, the Lebesgue measure is the standard way of assigning a volume to subsets of Euclidean space. ... In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ... The word complement (with an e in the second syllable, not to be confused with a different word, compliment with an i) has a number of uses. ...