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https://en.wikipedia.org/wiki/Finitism
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Finitism

Main idea[edit source]
The main idea of finitistic mathematics is not accepting the existence of infinite objects such as infinite sets. While all natural numbers are accepted as existing, the set of all natural numbers is not considered to exist as a mathematical object.
Therefore quantification over infinite domains is not considered meaningful. The mathematical theory often associated with finitism is Thoralf Skolem's primitive recursive arithmetic.

History[edit source]
The introduction of infinite mathematical objects was a development in mathematics that occurred a few centuries ago. The use of infinite objects was a controversial topic among mathematicians.
The issue entered a new phase when Georg Cantor, starting in 1874, introduced what is now called naive set theory and used it as a base for his work on transfinite numbers. When paradoxes such as Russell's paradox,
Berry's paradox and the Burali-Forti paradox were discovered in Cantor's naive set theory, the issue became a heated topic among mathematicians.