Discussion about this post

User's avatar
Martin Mertens's avatar

"the hyperreal numbers” might reasonably be given meaning by taking it to refer to the surreal numbers"

Interesting. Usually the *smallest* instance of a type is the natural choice of representative.

Is there a transfer principle for the surreal numbers? Can any sufficiently large ordered field be endowed with a transfer principle?

Expand full comment
Martin Mertens's avatar

Can infinitely large positive integers in nonstandard analysis be identified with nonstandard natural numbers as described under Scott Aaronson's latest blog post? I.e. a certain Turing machine runs forever, but we can't prove it runs forever, so we can consistently assert that it halts. In this case the number of steps until it halts is a nonstandard natural number.

Expand full comment
3 more comments...

No posts