It is not immediately evident that all functions in Brouw... — Carmelics

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

Modality & Possibility

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1 reason for

2 reasons against

Reasons For

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Reason for

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1.Brouwer's concept of function is less restrictive than Weyl's.
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2.Brouwer did not dismiss the possibility that discontinuous functions could be defined on proper parts of a continuum.
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Reasons Against

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Reason against 1 of 2

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1.Brouwer's continuity theorem, proven within intuitionistic mathematics, entails that every total function from the continuum to naturals is continuous.
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2.Any function defined on a spread in Brouwer's sense must be determined by finite initial segments of choice sequences, which structurally necessitates continuity.
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3.The bar theorem and fan theorem, central to Brouwer's own mathematical practice, collectively enforce continuity on all functions defined over the full continuum.
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Reason against 2 of 2

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