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/sci/ - Science & Math

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7469958 No.7469958 [Reply] [Original]

What is the best construction of the reals in your opinion? Dedekind cuts feels a lot more concrete than equivalence class of Cauchy sequences. However, completion of a metric space is a more general construction.

>> No.7469966
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7469966

>>7469958


Peter Johnstone: "Topos-theoretic models of the continuum"

https://www.youtube.com/watch?v=pKWYa9sc5UI

dedekind cuts in constructive settings [hott, or synthetic topology] will give you the locale of the real numbers with the expected topology

>> No.7469967

>>7469966
Why do you post that picture all the time? Also, thank you for introducing me to the "Math is Art" blog.

>> No.7469976
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7469976

>>7469958
>What is the best construction of the reals in your opinion?
The best construction is no construction.

>> No.7469978

>>7469966
looks cool but it is beyond me. why is it superior?

>> No.7470034

>>7469966
toposfu?

>> No.7470058

>>7469978
constructive predicative logics are more general and the theorems as well as the proofs are far more intuitive

>>7469976

I am more and more finitist as the time goes by