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*Subject*: RE: [amsat-bb] 0^0 - lets zero in on something else, alright? (pun intended)*From*: "Bill Jones" <wejones@xxxxxxxxxxxx>*Date*: Tue, 17 Nov 1998 10:59:18 -0500*In-reply-to*: <000201be11e5$d1350b50$853247cf@homedad.uthscsa.edu>

> 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. +----------------------------------------------+ | Bill Jones, N3JLQ,Sweden, Maine Zone 4 1/2 | | wejones@megalink.net | | http://www.megalink.net/~wejones | +----------------------------------------------+ ---- Via the amsat-bb mailing list at AMSAT.ORG courtesy of AMSAT-NA. To unsubscribe, send "unsubscribe amsat-bb" to Majordomo@amsat.org

**References**:**0^0 - lets zero in on something else, alright? (pun intended)***From:*B Keyport

**RE: 0^0 - lets zero in on something else, alright? (pun intended)***From:*Kevin Muenzler WB5RUE

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