A function on Brouwer's continuum that were discontinuous would require completed infinite information at a point, contradicting the temporal, constructive nature of choice sequences.

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Brouwer's continuum(as used in mathematics and logic): A way of thinking about the number line (all real numbers) developed by mathematician L.E.J. Brouwer, where numbers aren't all pre-existing but rather come into being as we construct them step-by-step.
Constructive (nature)(as used in philosophy of mathematics): Built or created step-by-step through actual processes, rather than assumed to exist all at once as abstract objects.
Discontinuous (function)(as used in mathematics): A mathematical relationship where there are sudden jumps or breaks—unlike a smooth, unbroken curve.
L.E.J. Brouwer(the philosopher behind Brouwerian criticism): A Dutch mathematician and philosopher (1881-1966) who believed mathematics is about what the human mind can actually build or understand, not just abstract symbols on paper.

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