4 ms·
That definitely is a more clean way to look at the matter, yes. Nonetheless I've seen the definition I stated above a few times and the merit is that you do not
by Perseids 13y ago
That definitely is a more clean way to look at the matter, yes. Nonetheless I've seen the definition I stated above a few times and the merit is that you do not have to take an implicit indirection every time you state something like "2≠0". And as a ring homomorphism ℤ->R for any ring R with identity element is already completely defined and in effect identical to the definition "2:=1+1…" for every positive whole number, it is really just a different way of formulating the same idea.
- pavelrub 13y agoMy point is that when talking about the definition of 2, it is enough to restrict ourselves to the natural numbers - since that is where 2 is coming from. If we then want to extend this symbol to other places - the meaning of such an extension will be given by a map, not by requiring a different definition. That is - there is only one 2, everything else is ψ(2) for the homomorphism ψ:Z->R.