@St_Rev Given f: σ→𝛕, there’s an obvious natural induced mapping f: 𝛕→N, the count of how many times an element of 𝛕 appears in range.
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Replying to @Meaningness
@Meaningness That's actually a pretty strong rigidity property, I think.2 replies 0 retweets 0 likes -
Replying to @St_Rev
@Meaningness eg f: R -> [0,1) given by f(x) = x mod 11 reply 0 retweets 0 likes -
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Replying to @St_Rev
@Meaningness (rigidity is borrowed from geometry; fewer allowed functions makes your geometry 'stiffer', more makes it 'floppier')2 replies 0 retweets 0 likes -
Replying to @Meaningness
@Meaningness Be interested to see a formalism that, intuitively, starts 'here' and works 'out' rather than goes up from a foundation.2 replies 0 retweets 0 likes -
Replying to @Meaningness
@St_Rev Example from the paper is that Dedekind cuts and Cauchy sequences are *not* real numbers as working mathematicians think about them.1 reply 0 retweets 0 likes
@St_Rev You should be able to just say what reals do without having to specify an “implementation”.
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Replying to @Meaningness
@St_Rev Non-standard reals get you that, but you need several metric tons of cast-iron machinery.1 reply 0 retweets 0 likes -
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