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Q: Why does zero to a negative power yield infinity rather than undefined?

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Value of log 0 is negative infinity (undefined). Because no power can give an answer of zero. it is in fact undefined but written as negative infinity for symbolizing. Otherwise undefined and infinity are two different things.

it is a domain error when trying to take 0 to the -1 power, but other negative powers are still just 0 (the same as positive) I'm not sure why -1 isn't though.I guess that's what the calculator said. Taking zero to a negative one power (or any negative power) is the same as 1 divided by 0, which is undefined. You could say it's infinity, but the limit does not exist.If you approach from the right (positive side) you go towards positive infinity.If you approach from the left (negative side) you go towards negative infinity.

Infinity is as big as you can get, so there is no number after it.There is also a "negative infinity" going the other way, so the total number of integers could be considered as two infinity (2 x ∞), or two ∞ plus 1 if you include zero. But usually infinity is defined to include the entire set of integers.* * * * *Except that infinity plus infinity, or even infinity times infinity is still infinity. However, infinity to the power of infinity is a higher level of infinity (Aleph1 rather than Aleph0). And if that does not do your head in, there is a lot more to the mathematics of infinities.

10 (or e) to the power of x range from zero to infinity. Lets try the extreme cases: 10^infinity = infinity 10^0 = 1 10^-infinity = 1/infinity = 0

Infinity.

E to the power infinity, or lim en as n approaches infinity is infinity.

Infinity.

As x tends to negative infinity, the expression is asymptotically 0.

Infinity

Infinity.

infinity

Congress does not have "undefined" powers. Review: The United States Constitution and Amendments #9 and #10.

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