What is Zero Raised to Itself?

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The discussion centers on the mathematical expression of zero raised to itself, 0^0, which is widely considered indeterminate. Participants explore different logical frameworks, including Boolean and fuzzy logic, to understand the implications of this expression. Some argue that in certain contexts, such as cardinal numbers or limits, 0^0 can be defined as 1, while others maintain that it remains undefined or indeterminate in standard arithmetic. The conversation highlights the complexity of defining 0^0 and the necessity of context in mathematical discussions. Ultimately, the consensus leans towards recognizing 0^0 as indeterminate, emphasizing the need for further exploration in specific mathematical frameworks.
  • #31
Originally posted by jcsd
No, you can only really use the formula to find a Fibonacci number when n is a natural number. But as F2 = 1 and F1 = 1, you can define F0 as 0 from the recurssive formula and this is how it is conventially defined.

0/1 is undefined and it's pretty easy to show that it cannot be a real or a complex number and thus you cannot perform algebraic operations on it.

A good point. Using Fibinocci it can not be proven.

Not using Fibinocci, rather using set theory,
is there a quantity of 1 of the set [undefined]
x a quantity of 1 of the set [undefined]

might that = 1?

If it were so, then 0 x 0 = 1
0 x 1 = 0

Would there be such a thing as -0 ?
If so, what would it be?
 
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  • #32
S = k log w wrote:
O/1 is infinity, or indeterm., or undefined, or whatever.

and then
jcsd wrote:
0/1 is undefined and it's pretty easy to show that it cannot be a real or a complex number and thus you cannot perform algebraic operations on it.

Am I missing something? I have been suffering under the delusion that 0/1 was equal to 0 for some years! Or is it possible that you meant either 1/0 or 0/0??
 
  • #33
Oops back to school for a good dose of reading comphrehension for me, I thought it was 1/0 (though why I wrote 0/1 I don't know).
 
  • #34
This is really interesting.

Look at this:

SQRT AND SQUARE


((+2)+(+2)) = +2^2
((-2)+(-2)) = -2^2
((+2)+(-2)+(+2)+(-2)) = 0^2

0^0 = ?
 
  • #35
Originally posted by S = k log w
This is really interesting.

Look at this:

SQRT AND SQUARE


((+2)+(+2)) = +2^2
((-2)+(-2)) = -2^2
((+2)+(-2)+(+2)+(-2)) = 0^2

0^0 = ?

Umm, ((-2)+(-2)) = -2^2? Want to rethink?
 
  • #36
Originally posted by selfAdjoint
Umm, ((-2)+(-2)) = -2^2? Want to rethink?
I think (hope) he meant -(2^2).

Don't forget PEMDAS...

- Warren
 
  • #37
Originally posted by chroot
I think (hope) he meant -(2^2).

Don't forget PEMDAS...

- Warren

Thank you.
 

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