Quantcast Factorial zero; Power of zero; Infinity - XP Math - Forums
XP Math Home Sign Up FREE! | Sign In | Classroom Setup | Common Core Alignment PDF Version

Go Back   XP Math - Forums > Welcome > Off-Topic Discussion

 
 
Thread Tools Display Modes
Old 12-04-2010   #1
Lisasmith111
 
Join Date: Nov 2010
Posts: 36
Default 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
Lisasmith111 is offline  
Old 12-06-2010   #2
MAS1

 
Join Date: Dec 2008
Posts: 249
Default

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

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
Lisasmith111 is offline  
 

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -4. The time now is 08:30 PM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, vBulletin Solutions Inc.
XP Math