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Properties of Natural Numbers

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Let m denote a natural number. Use any properties of the natural numbers to argue that m x m is not equal to m + m.

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Solution Summary

The properties of natural numbers are determined. The expert uses the properties to argue that m x m is not equal to the m + m.

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You want to show that if m is a natural number (0, 1, 2, 3, ...), then m x m is not equal to m + m. You can do this simply by showing that it is not in at least one case (because if it's not true for at least one natural number, then it's not true for natural numbers in general.

Look at some cases:

m = 0
m x m = 0
m + m = 0
m x m equals m + m

m = 1
m x m = 1
m + m = 2
m x m is not equal ...

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