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# Infinity

Infinity is the property of something limitless.

It is represented by the symbol ${\displaystyle \infty }$, introduced in the 17th century by the English mathematician John Wallis.

The word "infinity" comes from Latin infinitas, meaning “boundless”. In the sentence “There is no more than X apples in this bag”, if one can't replace X with any fixed number (even immensely large), then the bag contains an infinite collection of apples.

Various fields study infinity or its consequences: mathematics of course (where it is best understood), but also physics and philosophy.

Mathematically speaking, infinity is generally related to sets (the formal concept of a bag) in what is called the set theory. Let S be a set: S is infinite if (and only if):

• there is a strict subset T of S (i.e. T contains some, but not all, of the elements that S contains, and T does not contain any element that is not in S);
• there is a bijection between S and T (i.e. a way to associate every element in S to a distinct element in T).
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