in reply to zero to the power zero

It's undefined, because there's more than one solution. 1 is a good answer. But there are others, depending on how you approach the problem: is it x**x, 0**x, x**0 for x approaching 0? You get a different outcome every time.

It's not like the division 1/0, for which there is no finite answer.

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Re^2: zero to the power zero
by Moron (Curate) on Feb 19, 2007 at 10:39 UTC
    I don't see the different answers ... the limit is 1 for both x**x and x**0 as x -> 0 from above. 0**x goes undefined when x falls below 1, but that doesn't prove it stays undefined in the limiting case. So you get two answers agreeing on 1 and one failure to produce an answer out of the three cases. (misread as case of less than zero, as bart supposed, but ... )

    Update: I should refine this to: any function from the set of all f(x,y) = g(x)**h(y) that converges on 0**0 will either get a 1 or be discontinuous only at the exact 0,0 point. I used to have to prove that kind of thing as homework, but that's going back nearly 30 yrs!

    -M

    Free your mind

[reply]
      0**x goes undefined when x falls below 1
      Eh? The squareroot of 0 is still 0, AFAIK. And that's where the value of the exponent is 1/2: SQRT(0) == 0**0.5. I see no reason for a change in behaviour when x gets closer to 0.

      Perhaps you ment to say "when x falls below 0"? Because 0**x is 0 for any x > 0, and 0**x is infinite for any x < 0.

[reply]
[d/l]
      no all functions of this form converge
[reply]

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