Anyone remember how to solve 0^0?

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SUMMARY

The expression 0^0 is often left undefined in basic mathematics, but under specific conditions, it can be defined as 1. This conclusion arises from evaluating the limit of x^x as x approaches 0 from the positive side, which simplifies to e^(x log x) and ultimately converges to e^0, equating to 1. It is crucial to note that this function is not defined for negative real numbers unless one delves into multivalued complex functions.

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kings_gambit
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I remember it was 'one', but it's been a while...basically we want to find

lim (as x-->0) of (x^x), or not? Any takers?

Cheers,
 
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kings_gambit said:
I remember it was 'one', but it's been a while...basically we want to find

lim (as x-->0) of (x^x), or not? Any takers?

Cheers,


There's nothing "to solve". This is a problematic expression which in basic maths is almost always left undefined, and

sometimes, under some usually rather astringent conditions, it is defined as 1 because certainly
[tex]x^x=e^{x\log x}\xrightarrow [x\to 0^+]{} e^0=1[/tex]

Play attention to the fact the function isn't defined over the negative reals, unless you'd be wishing to get into multivalued complex functions and stuff.

DonAntonio
 
Please read https://www.physicsforums.com/showthread.php?t=530207
 
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