Factorial zero; Power of zero; Infinity - XP Math - Forums

 XP Math - Forums Factorial zero; Power of zero; Infinity

 12-04-2010 #1 Lisasmith111   Join Date: Nov 2010 Posts: 36 Factorial zero; Power of zero; Infinity Hello folks, Although 0! = 1 can anyone explain why this is the case. Hopefully, in a simple way so that I can understand why this is the case. Also why does anything to the power of zero = 1 eg 10^0 = 1 and 9^0 = 1. Finally, we all act as though we understand infinity even though none of us really know what it is. Can anyone explain? Kind regards Lisa Smith
12-06-2010   #2
MAS1

Join Date: Dec 2008
Posts: 249

Quote:
 Originally Posted by Lisasmith111 Hello folks, Although 0! = 1 can anyone explain why this is the case. Hopefully, in a simple way so that I can understand why this is the case. Also why does anything to the power of zero = 1 eg 10^0 = 1 and 9^0 = 1. Finally, we all act as though we understand infinity even though none of us really know what it is. Can anyone explain? Kind regards Lisa Smith
1. 0!
By definition n! = n x (n - 1) x (n - 2) x (n - 3) x ... x 2 x 1, or you can say:
n! = n x (n - 1)!
Dividing both sides by n gives:
n!/n = (n - 1)!

Now lets try some numbers:
Let n = 2.
2!/2 = (2 - 1)!
(2 x 1)/2 = 1!
2/2 = 1!
1 = 1!

Let n = 1.
1!/1 = (1 - 1)!
1/1 = 0!
1 = 0!

2. Power of Zero
1 = 2/2
1 = 2^1 / 2^1
When dividing the same "base" number with exponents, we subtract the exponents. In this example our base number is 2.
So,
1 = 2^(1 - 1)
1 = 2^0

3. Infinity
Infinity is a fascinating subject. In fact some infinities are bigger than others. A wonderful book about infinity and one mathematician's (Georg Cantor) obsession with it is "The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity". It can be found on Amazon.com at

http://www.amazon.com/Mystery-Aleph-...1674569&sr=1-2

MAS1

12-08-2010   #3
Lisasmith111

Join Date: Nov 2010
Posts: 36

Quote:
 Originally Posted by MAS1 1. 0! By definition n! = n x (n - 1) x (n - 2) x (n - 3) x ... x 2 x 1, or you can say: n! = n x (n - 1)! Dividing both sides by n gives: n!/n = (n - 1)! Now lets try some numbers: Let n = 2. 2!/2 = (2 - 1)! (2 x 1)/2 = 1! 2/2 = 1! 1 = 1! Let n = 1. 1!/1 = (1 - 1)! 1/1 = 0! 1 = 0! 2. Power of Zero 1 = 2/2 1 = 2^1 / 2^1 When dividing the same "base" number with exponents, we subtract the exponents. In this example our base number is 2. So, 1 = 2^(1 - 1) 1 = 2^0 3. Infinity Infinity is a fascinating subject. In fact some infinities are bigger than others. A wonderful book about infinity and one mathematician's (Georg Cantor) obsession with it is "The Mystery of the Aleph: Mathematics, the Kabbalah, and the Search for Infinity". It can be found on Amazon.com at http://www.amazon.com/Mystery-Aleph-...1674569&sr=1-2 MAS1
Thank you Mas1 for taking the time to explain. I will certainly look at the references you mention.

Lisa Smith

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