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Pronunciation varies by accent · noun
(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..
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.
Use finitism when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Finitism means (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..
The closest synonym depends on the sentence and intended sense.
The opposite depends on the specific sense.
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.
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