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Ultrafinitism (also called ultraintuitionism ) is a particularly strict interpretation of finitism in the philosophy of mathematics .

Ultrafinitists deal with the construction of mathematical objects taking into account the physical limitations of humans. Not only do they, like other followers of finitism , reject the existence of mathematical structures, the construction of which would require an infinite number of steps (as with the set of natural numbers ), but they also doubt the meaning of numbers such as (the greatest natural Number smaller than Skewes' number ). They justify this with the fact that nobody has calculated this number yet and that it may not be physically possible to calculate it. The number of elementary particles in the observable universe is estimated at , while Skewes' number is at .

Although ultrafinitism is a form of mathematical constructivism , it is viewed by the vast majority of constructivists as impractical. The constructive logician AS Troelstra formulated this in Constructivism in Mathematics ( 1988 ): “There is currently no satisfactory development” (“no satisfactory development exists at present”).

Alexander Jessenin-Wolpin had been a leading exponent of ultrafinitism since 1959 .

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