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Old 12-08-2010   #3
Lisasmith111
 
Join Date: Nov 2010
Posts: 36
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Quote:
Originally Posted by MAS1 View Post
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.

Thanks again for your post!

Lisa Smith
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