Post History
#2: Post edited
by
Quintec
·
2022-01-12T16:28:38Z (almost 3 years ago)
english
How's it possible to arrange 0 objects? How can 0! = 1?
1. I don't grok the following explanation. Isn't it physically impossible to "arrange 0 objects", or nothing? It's senseless to moot the concept of arrangement when you have nothing, like in a vacuum!- 2. [Division by zero is undefined](https://matheducators.stackexchange.com/a/5663) because you can't divide something (e.g. cookies) by nothing (no humans to divide the cookies for). Analogously then, why isn't 0! undefined too?
- >One more thing about permutations: it's convenient to have a definition for 0!, which is the number of ways to arrange 0 objects in a row. But there's only one way to arrange zero objects in a row: do nothing! So 0! = 1.
- David Patrick, [BS Math & Computer Science, MS Math (Carnegie Mellon), PhD Math (MIT)](https://artofproblemsolving.com/wiki/index.php/David_Patrick). *Introduction to Counting & Probability* (2005), p 18.
- 1. I don't understand the following explanation. Isn't it physically impossible to "arrange 0 objects", or nothing? It's senseless to raise the concept of arrangement when you have nothing, like in a vacuum!
- 2. [Division by zero is undefined](https://matheducators.stackexchange.com/a/5663) because you can't divide something (e.g. cookies) by nothing (no humans to divide the cookies for). Analogously then, why isn't 0! undefined too?
- >One more thing about permutations: it's convenient to have a definition for 0!, which is the number of ways to arrange 0 objects in a row. But there's only one way to arrange zero objects in a row: do nothing! So 0! = 1.
- David Patrick, [BS Math & Computer Science, MS Math (Carnegie Mellon), PhD Math (MIT)](https://artofproblemsolving.com/wiki/index.php/David_Patrick). *Introduction to Counting & Probability* (2005), p 18.
#1: Initial revision
by
DNB
·
2022-01-10T00:06:59Z (almost 3 years ago)
How's it possible to arrange 0 objects? How can 0! = 1?
1. I don't grok the following explanation. Isn't it physically impossible to "arrange 0 objects", or nothing? It's senseless to moot the concept of arrangement when you have nothing, like in a vacuum! 2. [Division by zero is undefined](https://matheducators.stackexchange.com/a/5663) because you can't divide something (e.g. cookies) by nothing (no humans to divide the cookies for). Analogously then, why isn't 0! undefined too? >One more thing about permutations: it's convenient to have a definition for 0!, which is the number of ways to arrange 0 objects in a row. But there's only one way to arrange zero objects in a row: do nothing! So 0! = 1. David Patrick, [BS Math & Computer Science, MS Math (Carnegie Mellon), PhD Math (MIT)](https://artofproblemsolving.com/wiki/index.php/David_Patrick). *Introduction to Counting & Probability* (2005), p 18.