Why 0!=1, or we can say, “Wow! 0! = 1 !!!!!,” or we can say, “Wow,!, 0!=1!” But why?

From Mathandmultimedia.com

Many books will tell you that equals is a definition. There are actually a few reasons why this is so – the two of which are shown below.

**Explanation 1:**

Based on my

Introduction to Combinations post, we can conclude that

taken

at a time is equal to

. This means, that there is only one way that you can group

objects from

objects. For example, we can only form one group consisting of

letters from

*A*,

*B, C* and

*D *using all the 4 letters.

From above, we know that the . But, . To satisfy the equation, must be equal to .

**Explanation 2:**

We can also use the fact that . Dividing both sides by , we have . If we let , we have which is what we want to show.

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Tags: 0!, combinations, combinatorics, factorials, permutations

This entry was posted on June 18, 2012 at 8:59 am and is filed under Honors Alg. 2, Precalculus, Statistics, Statistics Readings. You can follow any responses to this entry through the RSS 2.0 feed.
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