Algebra

Absolute Value Property

In this post, I prove that $ |xy| = |x||y|$ in which $x$ is a variable for any real number and $y$ is a variable for any real number. This is done by approximately following the steps in reference [1]. Then I provide a lot of commentary because that is what I like to do. …

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Exponents

The following rules apply for exponents that are positive integers. The justification is sketched here.   These rules are also said to apply for exponents that are not positive integers–that is, zero and negative integers. If $ p$ and $ q$ are rational numbers, they are also said to apply. Finally, if $ p$ and …

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