Timeline for Why do we ignore non-standard finite sets in ordinary mathematics?
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| Mar 19, 2012 at 22:00 | comment | added | Mike Shulman | I think this is really the point. When we say "a natural number", we mean a natural number in the current theory, which includes any non-standard ones. Most people don't bother to say "by induction" for "obvious" facts about N, but almost always if you pressed them, that's what they would say they meant. This is the same as the rest of math; we can't write all the details or papers would be unmanageably long. But that doesn't mean all proofs should be regarded as "non-rigorous", except in the sense that they still require "compiling" to become fully formalized. | |
| Mar 18, 2012 at 16:02 | history | answered | Andrej Bauer | CC BY-SA 3.0 |