Comments on: Understanding Exponents (Why does 0^0 = 1?) http://betterexplained.com/articles/understanding-exponents-why-does-00-1/ Learning shouldn't hurt. Let's share the insights that made difficult ideas click. Thu, 11 Mar 2010 15:20:58 +0000 http://wordpress.org/?v=2.8.4 hourly 1 By: Kalid http://betterexplained.com/articles/understanding-exponents-why-does-00-1/#comment-274935 Kalid Tue, 09 Mar 2010 07:19:08 +0000 http://betterexplained.com/articles/understanding-exponents-why-does-00-1/#comment-274935 @Jonathan: Thanks for the comment! Yes, that's another, more detailed/combinatorial way to think about it. Depending on the context of the problem, growth or combinations may make sense. Often times people see e^x and are trying to figure out the meaning of a 0 exponent; other times, you have n^m (n choices, m decision) and this interpretation helps too. @Jonathan: Thanks for the comment! Yes, that’s another, more detailed/combinatorial way to think about it. Depending on the context of the problem, growth or combinations may make sense. Often times people see e^x and are trying to figure out the meaning of a 0 exponent; other times, you have n^m (n choices, m decision) and this interpretation helps too.

]]> By: Jonathan Gallagher http://betterexplained.com/articles/understanding-exponents-why-does-00-1/#comment-274920 Jonathan Gallagher Mon, 08 Mar 2010 22:16:09 +0000 http://betterexplained.com/articles/understanding-exponents-why-does-00-1/#comment-274920 Here is a possibly more simple understanding of why 0^0 = 1 (depending on your point of view). Take a total map to be a function that is defined on every point in the domain. Then, We can think of n^m as the number of total maps (ahem functions) from the m element set to the n element set. To see this draw 2 circles, but n dots in one and m dots in the other (it is advisable to pick small n and m!). Then very methodically draw all possible total maps. Maybe make a tree. Now, the empty set is a subset of every set, thus there is always a map from the empty set to any set. Moreover, this map is unique. It follows that there is a map from the empty set to the empty set, and this map is unique. Then the number of maps from the 0 element set to the 0 element set is 1. Thus 0^0 = 1. Here is a possibly more simple understanding of why 0^0 = 1 (depending on your point of view).

Take a total map to be a function that is defined on every point in the domain.

Then,
We can think of n^m as the number of total maps (ahem functions) from the m element set to the n element set. To see this draw 2 circles, but n dots in one and m dots in the other (it is advisable to pick small n and m!). Then very methodically draw all possible total maps. Maybe make a tree.

Now, the empty set is a subset of every set, thus there is always a map from the empty set to any set. Moreover, this map is unique. It follows that there is a map from the empty set to the empty set, and this map is unique. Then the number of maps from the 0 element set to the 0 element set is 1. Thus

0^0 = 1.

]]> By: Sully http://betterexplained.com/articles/understanding-exponents-why-does-00-1/#comment-273297 Sully Wed, 24 Feb 2010 20:09:28 +0000 http://betterexplained.com/articles/understanding-exponents-why-does-00-1/#comment-273297 This material is incredibly easy to digest and apply. Do you have any material on logarithms in general? This material is incredibly easy to digest and apply. Do you have any material on logarithms in general?

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