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### Why “characteristic zero” and not “infinite characteristic”?

The characteristic of a ring (with unity, say) is the smallest positive number $n$ such that $$\underbrace{1 + 1 + \cdots + 1}_{n \text{ times}} = 0,$$ provided such an $n$ exists. Otherwise, we ...
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### Is this $\gcd(0, 0) = 0$ a wrong belief in mathematics or it is true by convention?

I'm sorry to ask this question but it is important for me to know more about number theory. I'm confused how $0$ is not divided by itself and in Wolfram Alpha $\gcd(0, 0) = 0$ . My question here is: ...