What is Zero Raised to Itself?

  • Context: Undergrad 
  • Thread starter Thread starter Shinobiku
  • Start date Start date
  • Tags Tags
    Zero
Click For Summary
SUMMARY

The discussion centers on the mathematical expression of zero raised to itself, denoted as 0^0. Participants agree that 0^0 is classified as "indeterminate," differing from "undefined." The conversation highlights various contexts in which 0^0 can be interpreted, including Boolean logic, fuzzy logic, and cardinal numbers, where 0^0 can equal 1. Ultimately, the consensus is that the expression lacks a definitive value without additional context.

PREREQUISITES
  • Understanding of Boolean logic and fuzzy logic
  • Familiarity with limits in calculus
  • Knowledge of cardinal numbers and set theory
  • Basic principles of exponentiation
NEXT STEPS
  • Explore the implications of indeterminate forms in calculus
  • Study the properties of cardinal numbers and their operations
  • Investigate the definitions and applications of Boolean and fuzzy logic
  • Learn about the conventions used in polynomial and power series regarding 0^0
USEFUL FOR

Mathematicians, educators, students in advanced mathematics, and anyone interested in the nuances of mathematical definitions and their implications in various contexts.

  • #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?
 
Mathematics news on Phys.org
  • #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.
 

Similar threads

  • · Replies 47 ·
2
Replies
47
Views
6K
  • · Replies 31 ·
2
Replies
31
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 13 ·
Replies
13
Views
974
  • · Replies 12 ·
Replies
12
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 16 ·
Replies
16
Views
5K
  • · Replies 63 ·
3
Replies
63
Views
6K