Why is the number 1 subject to different rules in math

[RayMan]

@Thudlow Boink

I think you’re thinking of the Fundamental Theorem of Arithmetic. The Fundamental Theorem of Algebra is something different.

Thank you, you’re absolutely right.

[David_Simmons]

@Wesley Clark

but ‘logically’ if you square or take the root of any number other than 1 you get a different number than the original. 1 is the only number that doesn’t apply to and i didn’t see why exactly.

Your question was “Why different rules for 1?” and it is being pointed out that there aren’t different rules. 1[sup]2[/sup] means 11 just like 2[sup]2[/sup] means 22.

sqrt(1) means a number which when multiplied by itself gives 1 just like sqrt(2) means a number which when multiplied by itself gives 2.

The thing regarding 1 that doesn’t apply to other numbers is that there exists a number, x, such that n*x = n as someone already pointed out. And that, I think, is a postulate, or maybe a definition and not a rule.