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this post was submitted on 07 May 2024
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It is a natural number. Is there an argument for it not being so?
no it's not
Well I’m convinced. That was a surprisingly well reasoned video.
Thanks for linking this video! It lays out all of the facts nicely, so you can come to your own decision
There can't really be an argument either way. It's just a matter of convention. "Natural" is just a name, it's not meant to imply that 1 is somehow more fundamental than -1, so arguing that 0 is "natural" is beside the point
If we add it as natural number, half of number theory, starting from fundamental theorem of arithmetics, would have to replace "all natural numbers" with "all natural numbers, except zero".
Prime factorization starts at 2, I'm not sure what you mean. Anyway, if you wanted to exclude 0 you could say "positive integers", it's not that hard.
1 also has a unique 'empty' prime factorization, while zero has none.
You can also say "nonnegative integers", if you want to include zero.