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    Troelstra and van Dalen demonstrate in 'Constructivism in... — Carmelics
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    Challenges→It is not immediately evident that all functions in Brouwer's sense must be continuous.

    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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    Key Terms

    Choice-sequence definability(as another type of valid function definition)
    The ability to describe a function as a sequence of choices that unfolds over time, where each step is free to choose from options rather than following a fixed formula.
    Constructivism in Mathematics(as the title of their work)
    A philosophy of math that says something only truly exists if we can actually construct or build it step-by-step, rather than just proving it logically.
    Discontinuous cases(as the type of functions being ruled out)
    Mathematical functions that have gaps or jumps in them—where small changes in input can cause huge unpredictable changes in output.
    Function-existence(as the main concept being analyzed)
    The question of what counts as a real, valid function (a mathematical rule that transforms inputs into outputs) and when we can say it genuinely exists.

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    Intuitionistic(as a logical framework)
    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.

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    Truth & Knowledge1 linkedModality & Possibility1 linked

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    It is not immediately evident that all functions in Brouwer's sense must be cont...

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