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Finitism

Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects. It is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects (e.g., infinite sets) are accepted as legitimate.

Wiktionary

finitism

n. (context mathematics English) An extreme form of constructivism, according to which a mathematical object does not exist unless it can be constructed from natural numbers in a finite number of steps.