英和和英

名詞

finitism (uncountable)

1. (mathematics, philosophy) 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.
   • 2025 August 4, Manon Bischoff, “Some Mathematicians Don’t Believe in Infinity”, in Scientific American‎, archived from the original on 5 August 2025:

     As a result, some logical principles no longer apply, including Aristotle’s theorem of the excluded middle, according to which a mathematical statement is always either true or false. In finitism, a statement can be indeterminate at a certain point in time if the value of a number has not yet been determined. For example, with statements that revolve around numbers such as 0.999..., if you carry out the full period and consider an infinite number of 9’s, the answer becomes 1. But if there is no infinity, this statement is simply wrong.

派生語

• finitist
• ultrafinitism