Infinity (∞)
The concept of a quantity without bound — and, in modern math, of multiple distinct sizes of unboundedness.
Origin
Aristotle distinguished 'potential' infinity (you can always add one more) from 'actual' infinity (a completed endless thing), and rejected the second. Georg Cantor in the 1870s proved that there are multiple, genuinely different infinities — the integers and the reals are both infinite but the reals are 'more' infinite. The lemniscate symbol ∞ was introduced by John Wallis in 1655. Cantor's work was so disturbing to other mathematicians (and to him) that he ended his life in and out of asylums.
Modern usage
The most-overused mathematical word in English — 'infinity pool,' 'infinite scroll,' 'to infinity and beyond.' Real mathematical infinity is the topic of every other pop-math book. 'Hilbert's hotel' (the infinite hotel that can always fit more guests) is the canonical YouTube-math demonstration.
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