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In the philosophy of mathematics , finitism is a form of constructivism , according to which a mathematical object can only be meaningfully talked about if it is derived from natural numbers in a finite (or, in a weakened variant, countably infinite ) number of steps can. A typical representative was Leopold Kronecker .

Ultrafinitism (or ultraintuitionism), as represented by Alexander Jessenin-Wolpin , is even stricter than finitism . This requires a constructability not only in a finite number of steps, but in a physically possible number of steps.

The discrete mathematics dealing with finite or most countable mathematical structures. This leads to a certain overlap between finitism and discrete mathematics, although the latter need not be based on finitistic motives.