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0^0 = 1?
04-25-2017, 11:14 AM (This post was last modified: 04-25-2017 11:22 AM by AlexFekken.)
Post: #22
RE: [wp34s] 0^0 = 1?
"Now take lim (x->0) f(x)/g(x), where f(x) and g(x) are nice, well-behaved functions..."

Actually, making these assumptions is changing the problem. The original problem is the behaviour of x^y near (x=0, y=0) and whether that justifies defining 0^0 to be 1. No f's, no g's and certainly no assumptions that these function need to be so nice that they behave like polynomials around (0, 0).

The examples (even just considering those with both x and y positive real numbers and choosing principal values) clearly show that (uniquely) defining 0^0 is a bad choice.

The only justification given so far for choosing 0^0 to be 1 comes from a context in which y is limited to integers, e.g. looking at power series (including polynomials) and making it easy to write the general term with a variable exponent without making an exception for an exponent of 0. This is certainly not a numerical context but an algebraic one and so it seems irrelevant when we are talking about numerical evaluations.
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Messages In This Thread
0^0 = 1? - emece67 - 04-21-2017, 07:43 AM
RE: [wp34s] 0^0 = 1? - Werner - 04-21-2017, 09:55 AM
RE: [wp34s] 0^0 = 1? - Thomas Okken - 04-21-2017, 01:54 PM
RE: [wp34s] 0^0 = 1? - Egan Ford - 04-22-2017, 01:02 AM
RE: [wp34s] 0^0 = 1? - Chris Dreher - 04-22-2017, 05:52 PM
RE: [wp34s] 0^0 = 1? - Werner - 04-22-2017, 08:00 AM
RE: [wp34s] 0^0 = 1? - Thomas Okken - 04-22-2017, 11:35 AM
RE: [wp34s] 0^0 = 1? - emece67 - 04-22-2017, 09:43 AM
RE: [wp34s] 0^0 = 1? - AlexFekken - 04-22-2017, 10:40 PM
RE: [wp34s] 0^0 = 1? - Thomas Okken - 04-22-2017, 11:28 PM
RE: [wp34s] 0^0 = 1? - AlexFekken - 04-23-2017, 01:06 AM
RE: [wp34s] 0^0 = 1? - AlexFekken - 04-23-2017, 01:46 AM
RE: [wp34s] 0^0 = 1? - Thomas Okken - 04-23-2017, 02:58 PM
RE: [wp34s] 0^0 = 1? - Claudio L. - 04-23-2017, 07:33 PM
RE: [wp34s] 0^0 = 1? - Thomas Okken - 04-23-2017, 07:45 PM
RE: [wp34s] 0^0 = 1? - Claudio L. - 04-24-2017, 12:40 AM
RE: [wp34s] 0^0 = 1? - Thomas Okken - 04-24-2017, 02:09 AM
RE: [wp34s] 0^0 = 1? - BobVA - 04-23-2017, 04:41 PM
RE: [wp34s] 0^0 = 1? - Chris Dreher - 04-24-2017, 03:45 AM
RE: [wp34s] 0^0 = 1? - Thomas Okken - 04-24-2017, 04:26 AM
RE: [wp34s] 0^0 = 1? - Chris Dreher - 04-24-2017, 06:24 AM
RE: [wp34s] 0^0 = 1? - AlexFekken - 04-25-2017 11:14 AM
RE: [wp34s] 0^0 = 1? - Felix Gross - 04-25-2017, 03:00 PM
RE: [wp34s] 0^0 = 1? - emece67 - 04-25-2017, 07:53 PM
RE: [wp34s] 0^0 = 1? - EdS2 - 04-26-2017, 06:03 AM
RE: [wp34s] 0^0 = 1? - Chris Dreher - 04-27-2017, 04:55 AM
RE: [wp34s] 0^0 = 1? - Paul Dale - 04-26-2017, 06:40 AM
RE: 0^0 = 1? - emece67 - 05-03-2017, 03:24 PM
RE: [wp34s] 0^0 = 1? - Gerald H - 04-27-2017, 05:48 AM
RE: [wp34s] 0^0 = 1? - d b - 04-27-2017, 03:35 PM
RE: [wp34s] 0^0 = 1? - rprosperi - 04-27-2017, 04:28 PM
RE: [wp34s] 0^0 = 1? - emece67 - 04-27-2017, 05:32 PM
RE: 0^0 = 1? - Felix Gross - 04-27-2017, 08:01 PM
RE: 0^0 = 1? - Dwight Sturrock - 04-27-2017, 11:20 PM
RE: 0^0 = 1? - Craig Bladow - 04-27-2017, 11:46 PM
RE: 0^0 = 1? - matthiaspaul - 04-27-2017, 11:51 PM
RE: 0^0 = 1? - ttw - 04-28-2017, 04:57 AM
RE: 0^0 = 1? - Chris Dreher - 04-28-2017, 04:50 PM
RE: 0^0 = 1? - Han - 04-28-2017, 05:50 PM
RE: 0^0 = 1? - matthiaspaul - 04-28-2017, 10:22 PM
RE: 0^0 = 1? - pier4r - 04-28-2017, 07:39 AM
RE: 0^0 = 1? - AndiGer - 04-28-2017, 07:18 PM
RE: 0^0 = 1? - ttw - 04-30-2017, 12:35 AM
RE: 0^0 = 1? - brickviking - 04-30-2017, 04:59 AM
RE: 0^0 = 1? - Anderson Costa - 05-09-2017, 01:04 AM
RE: 0^0 = 1? - Felix Gross - 05-09-2017, 07:30 PM



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