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12042010  #1 
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 
12062010  #2  
Join Date: Dec 2008
Posts: 249

Quote:
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 

12082010  #3  
Join Date: Nov 2010
Posts: 36

Quote:
Thanks again for your post! Lisa Smith 

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