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The question is not whether you can define it in terms of addition in some abstract way, but whether you can define it in terms of repeated addition, i.e. somet
by alentist 6y ago
The question is not whether you can define it in terms of addition in some abstract way, but whether you can define it in terms of repeated addition, i.e. something of the form x + x + … + x.
- codethief 6y ago> The question is not whether you can define it in terms of addition in some abstract way This is splitting hairs. The reals themselves are defined "in some abstract way". For instance, what does addition of reals even mean? How do you add two arbitrary real numbers? Exactly, by adding the elements of the Cauchy sequences. (And similarly for multiplication.) This is the definition of addition (multiplication) and the only abstraction involved here is the abstraction due to the way the reals are constructed in the first place.
- alentist 6y ago> This is splitting hairs. Nope. The question addressed by the article is precisely whether multiplication is repeated addition. > adding the elements of the Cauchy sequences. (And similarly for multiplication.) This is the definition of addition (multiplication) Nope. See https://news.ycombinator.com/item?id=26336108 https://news.ycombinator.com/item?id=26336108.