Troelstra and van Dalen demonstrate in 'Constructivism in Mathematics' that intuitionistic function-existence requires lawlike or choice-sequence definability, ruling out discontinuous cases.
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A system of logic that rejects the idea that something must be either true or false if we can't actually verify which one it is; closely related to constructivism.
Lawlike definability(as one type of valid function definition)
The ability to describe a function using a fixed, deterministic rule—like a formula that always produces the same output for the same input.
Troelstra and van Dalen(as the authors being referenced)
Two mathematicians and logicians who studied how we can be certain that mathematical objects actually exist, rather than just assuming they do.