2

What is $0^0$ ?

I have read many debates about this question. The debate has been going on at least since the early 19th century. At that time, most mathematicians agreed that $0^0$ = 1, until in 1821 Cauchy listed $0^0$ along with expressions like $\frac{0}{0}$ in a table of undefined forms.

On Wikipedia, there is a thread for the same.

On Quora, i read a discussion about the same.

The question is not to explain for $0^0$=1 or $0^0$=0 or it is undefined.

What sholuld we conclude for defining $0^0$ ?

user1551
  • 139,064
Manoj
  • 1,757
  • 1
    ^That was Cauchy. Atleast when you can't give an answer, spell that great mathematician's name properly. – Manoj Mar 25 '13 at 12:05
  • 1
    It depends how you come to $0^0$. Is it a limit case of a sequence ${a_n^{b^n}}$ with $a_n \rightarrow 0$ and $b_n \rightarrow 0$ ? – Djaian Mar 25 '13 at 12:06
  • Symbols don't mean things unless we give them meaning. – anon Mar 25 '13 at 12:07
  • So, mathematically it is not defined. – Manoj Mar 25 '13 at 12:08
  • @sdcvvc: there stas needs an explanation for the question to why 0^0=1? – Manoj Mar 25 '13 at 12:14
  • 3
    No, I did not say it is not defined. It is defined differently in different contexts for very good reasons, in some contexts it is not defined, and these reasons are explained in the link that sdcvvc gave. (I do not know what the word "stas" means.) – anon Mar 25 '13 at 12:22
  • @anon: "stas" is the person who have asked for the explanation to 0^0=1 in that link. – Manoj Mar 25 '13 at 12:26
  • 1
    @Manoj: Please see the answers in the link, not only the question. – sdcvvc Mar 25 '13 at 12:28
  • Just going through them. – Manoj Mar 25 '13 at 12:42

0 Answers0