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## Main Question or Discussion Point

Does 0^0 equal one, or is it undefined?

- Thread starter Loren Booda
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- #1

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Does 0^0 equal one, or is it undefined?

- #2

chroot

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It's an indeterminate form. (It's many-valued; not the same as undefined.)

- Warren

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- #3

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Is the limit of sin(x), as x approaches infinity, also "indeterminate"?

- #4

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It does not exist because the values oscillate between 1 and -1.

- #5

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There are three interpretations (each one depends on context):

0^0 = 1, or indeterminate form, or undefined

The first is the set-theoretic interpretation. Justification?

Consider f:A->B. The set of all such functions is denoted B^A. In this context, {}^{} would represent the set of

functions f:{}->{}, and 0^0 would represent the number of functions in this set. There is only one such function.

(This is not the only justification for this particular interpretation, i.e., 0^0 = 1.)

It's a strange post. A cursory preliminary investigation would turn up something like the following:

http://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_power

0^0 = 1, or indeterminate form, or undefined

The first is the set-theoretic interpretation. Justification?

Consider f:A->B. The set of all such functions is denoted B^A. In this context, {}^{} would represent the set of

functions f:{}->{}, and 0^0 would represent the number of functions in this set. There is only one such function.

(This is not the only justification for this particular interpretation, i.e., 0^0 = 1.)

It's a strange post. A cursory preliminary investigation would turn up something like the following:

http://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_power

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- #6

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Plot y^x and x^y and see what you get as y->0. The answer clearly depends on the direction of approach.

- #7

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Just to add one very important interpretation of when 0^0 is defined to be 1: Power series.There are three interpretations (each one depends on context):

In power series, the form 0^0 must be taken to mean 1. If not, we would have to write [itex]\exp(x) = 1 + \sum_{n=1}^{\infty} x^n/n![/itex] rather than [itex]\exp(x) = \sum_{n=0}^{\infty} x^n/n![/itex]

- #8

Gib Z

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[tex](1+x)^n = \sum_{k = 0}^n \binom{n}{k} x^k[/tex]

Its not valid for x=0 except when defined 0^0 = 1

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