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anonymous
 3 years ago
0^0 = ?
anonymous
 3 years ago
0^0 = ?

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shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0yep, it is undefined.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1``` Prove that 0 to the 0 power is undefined. ``` Proof by contradiction. By definition, \(0^n = 0\). By definition, \(x^0 = 0\). But the two definitions contradict at \(x=0\) and \(n = 0\).

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Another one: Suppose that \(0^0 = x\). Then \(\log _ 0x = 0\). But there are infinite such values, so \(0^0\) does not exist.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1I meant to type that, sorry :(

shubhamsrg
 3 years ago
Best ResponseYou've already chosen the best response.0x^0 = x^(nn) = x^n /x^n so it'll be undefined whenever denominator is 0.
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