# RE: 0^0 - lets zero in on something else, alright? (pun intended)

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> Sure, by "definition" any number to the zero power is 1.  BUT by reason, and
> mathematics, zero to ANY power is still zero.  Right?  So which definition
> has precedence?
>

If you forget about trying to figure out what is "defined" and
try to "reason" what the answer is, the results are interesting.
Following the suggestion of another poster, I made an Excel
spread sheet and plotted 3 different graphs for x^y :
(1) I plotted for x=1.5 with y going toward zero;
(2) I plotted for y=0.01 with x going toward zero;
(3) I plotted for both x and y approaching zero;

Example (1) of course gave a graph that approached 1.000, as
expected. Ie, any number taken to the zero'th power is 1.00,
not so much by definition, but that is simply what the numbers
give.
Example (2) gives a graph that approaches zero. Ie as
a small number taken to a very small power gets closer and closer
to zero, the result approaches zero.
Example (3) gives a graph that approaches 1.000.  Ie, as both the
number and the power approach zero, the result approaches 1.000. This
one is not so not so clearcut though, since 2 variables are changing. It
might be interesting to see a 3-dimensional plot of these trends.

Overall though, you see the problem, ie that you have a conflict between
a trend that wants to approach zero and a trend that wants to
approach 1.000. I suspect that depending how you decide to vary
the x and y might affect the overall answer in the example where
both number and power are varied, ie if you have x approach zero
faster than y, or visa versa, the results could be different, and the
choice of HOW to vary x and y is somewhat arbitrary, thus the need for
either a "definition" that does not conflict with other known calculation
trends, or perhaps just a statement that that one example is not defined.
Interesting discussion.

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| Bill Jones, N3JLQ,Sweden, Maine  Zone 4 1/2  |