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johncena
- 131
- 1
what is the proof for the statement 0! = 1??
But zero is an even number since it has a parity of 0.monty37 said:a number neither odd nor even cannot be equal to an odd number.
gunch said:n! = (n-1)! * n for n > 0
Tac-Tics said:I'll also note a definition can never be wrong. It may be useless, but it's never wrong.
But that would be a useless definition!derek e said:... unless a useless definition is defined to be something that is incorrect or wrong. :tongue:
A definition cannot be incorrect or wrong. What a group of definitions can be is inconsistent, which is subtly different :) Determining if a set of axioms is consistent is a difficult problem (and consistency is the cornerstone for godel's theorem as with an inconsistent set of axioms you can prove stupid things like 0=1, 1=2, etc)derek e said:... unless a useless definition is defined to be something that is incorrect or wrong. :tongue:
Factorial is a mathematical operation denoted by an exclamation mark (!) and is used to find the product of a number and all the positive integers that are smaller than it. 0 factorial (0!) is defined as 1.
While it may seem counterintuitive, the definition of factorial (n!) includes the number 1 as a factor. Therefore, when n = 0, 0! is equal to 1.
The proof for 0! = 1 is based on the mathematical principle of induction. By using the definition of factorial, it can be shown that 1! = 1, and then using the induction step, it can be shown that (n+1)! = (n+1) * n! for all positive integers n. Substituting n = 0 in this equation gives 1 = (0+1) * 0!, which simplifies to 1 = 1 * 0!. Therefore, 0! = 1.
Yes, the concept of 0 factorial is used in various areas of mathematics and science, such as in the binomial theorem, combinatorics, and probability calculations. It also has applications in computer science and physics.
No, the definition of factorial and the mathematical proof both show that 0! = 1. Therefore, there are no exceptions to this rule.