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What is 0^0 equal to?

By Murray Bourne, 22 Jan 2009

In the introduction to Laws of Integral Exponents, I mention the debate about the value of 00. Is it zero or is it one?

Why is it a problem? Look at the following 2 patterns:

Multiply 0 as many times as you like, you get 0.

0^3 = 0
0^2 = 0
0^1 = 0
0^0 = 0

But then again, any number raised to the power 0 is 1:

3^0 = 1
2^0 = 1
1^0 = 1
0^0 = 1

That's why there is dispute about the value of 0^0.

On the page linked to before, I wrote:

It is most commonly regarded as having value 1

An interesting conundrum. Sometimes our wonderful, (normally) consistent system of math breaks down.

See the 42 Comments below.

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  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
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    \( \int g dx = \sqrt{\frac{a}{b}} \)
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