Is 0^0 defined or not?

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Original post by Boops
So is that the only one limit that sais the opposite of all the other ones, and is that why they say it''s undefined, but because all others say it''s 1, they defined it as 1 in Maple?

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Original post by Cedric

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Original post by Boops
So is that the only one limit that sais the opposite of all the other ones, and is that why they say it''s undefined, but because all others say it''s 1, they defined it as 1 in Maple?

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Strictly speaking, and AFAIK, it''s undefined.

Another related example is sin(x)/x. It''s undefined at x=0. But since this function is used so often, and its limit is 1, mathematicians have called it sinc(x), which is sin(x)/x if x!=0 and 1 if x = 0.

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telling me that it is 1.

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#include <iostream>
#include <stdlib.h>

int main()
{
    float answer=0^0;
    std::cout << "0^0="<< answer << std::endl;
    system("PAUSE");
    return 0;
}
  

#include <iostream>
#include <stdlib.h>
#include <math.h>

int main()
{
    //Thank you furby100
    std::cout << "0^0:" << pow(0,0) << std::endl;
    system("PAUSE");
    return 0;
}
 

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Original post by bigbadboo
but it doesnt make sense in practice

0 pies raised 0 times = 1 pie?

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Original post by Xiachunyi
Edit:

#include <iostream>
#include <stdlib.h>

int main()
{
    float answer=0^0;
    std::cout << "0^0="<< answer << std::endl;
    system("PAUSE");
    return 0;
}
  

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quote:

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Special cases include
(8) x¹ = x
and
(9) x⁰ = 1
for x != 0 . The definition 0⁰ = 1 is sometimes used to simplify formulas, but it should be kept in mind that this equality is a definition and not a fundamental mathematical truth (Knuth 1992; Knuth 1997, p. 56).

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