4 ms·
In general, what is a mathematical object? Is the natural numbers one?
by grandalf 10y ago
In general, what is a mathematical object? Is the natural numbers one?
- openasocket 10y agoIt's just a informal term for the things mathematicians study. So the natural numbers are mathematical objects, as well as a set, a function, a manifold, a vector space, etc.
- hasch 10y agoI think, it's an instance of a mathematical "idea". E.g. 7 is an object of the idea "prime numbers".
- dogecoinbase 10y agoThis is actually a surprisingly complex question in mathematical philosophy -- I unfortunately can't find a copy online right now, but if the idea of mathematical objects interests you I'd highly recommend Paul Benacerraf's 1965 paper "What Numbers Cannot Be", which explores the complexity of the idea of even a single integer as an "object".
- Cogito 10y agoFor those interested, the article is actually called "What Numbers Could not Be" (many references have "What Numbers Cannot Be" so maybe it was published under both names at some point?) There is a copy at: http://isites.harvard.edu/fs/docs/icb.topic1240846.files/Benacerraf.pdf http://isites.harvard.edu/fs/docs/icb.topic1240846.files/Ben...
- grandalf 10y agoThanks for posting that!
- dogecoinbase 10y agoThank you! I just checked my copy of Cambridge's Philosophy of Mathematics and it is indeed "could not" -- the PDF I have on my laptop, however, is "cannot". I wonder when/where that happened.