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/MysteryAleph...1674569&sr=12
MAS1