In the philosophy of mathematics, ultrafinitism, ultraintuitionism, strict formalism, strict finitism, actualism, predicativism, and strong finitism are various philosophies of mathematics with aspects of finitism and intuitionism. Common to these philosophies is their objection to the totality of number theoretic functions like exponentiation over natural numbers.
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In the philosophy of mathematics, ultrafinitism, ultraintuitionism, strict formalism, strict finitism, actualism, predicativism, and strong finitism are various philosophies of mathematics with aspects of finitism and intuitionism. Common to these philosophies is their objection to the totality of number theoretic functions like exponentiation over natural numbers.
==Main ideas== Like other finitists, ultrafinitists deny the existence of the infinite set \N of natural numbers, on the basis that it can never be completed.
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