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From: Marchal <marchal.domain.name.hidden>

Date: Mon Jan 17 03:48:40 2000

Hal:

*>Rational numbers are continuous, by the typical definition. Between
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*>any two rational numbers there is another (and therefore, an infinite
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*>number of others).
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This is density. Q is dense indeed, but highly discontinuous.

Continuity means either that all dedekind-cut define numbers, or that

all cauchy sequences define numbers.

Note that in classical analysis these two definitions are equivalent,

but in intuitionistic mathematics they are not!

Unlike computability, continuity like provability is a relative

concept.

Bruno.

Received on Mon Jan 17 2000 - 03:48:40 PST

Date: Mon Jan 17 03:48:40 2000

Hal:

This is density. Q is dense indeed, but highly discontinuous.

Continuity means either that all dedekind-cut define numbers, or that

all cauchy sequences define numbers.

Note that in classical analysis these two definitions are equivalent,

but in intuitionistic mathematics they are not!

Unlike computability, continuity like provability is a relative

concept.

Bruno.

Received on Mon Jan 17 2000 - 03:48:40 PST

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