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Shadowys
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undefined. 0/0=?
shubhamsrg
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yep, it is undefined.
ParthKohli
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```
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
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Another one:
Suppose that \(0^0 = x\). Then \(\log _ 0x = 0\). But there are infinite such values, so \(0^0\) does not exist.
sauravshakya
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@ParthKohli
x^0 =1
ParthKohli
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Whoopsie.
ParthKohli
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I meant to type that, sorry :-(
ranyai12
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it's undefined
shubhamsrg
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x^0 = x^(n-n) = x^n /x^n
so it'll be undefined whenever denominator is 0.