Real modulus/Introduction/Section

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For a real number , the modulus is defined in the following way.

So the modulus (also called the absolute value) is never negative and has only at the value , elsewhere it is always positive. The mapping

is called the modulus function. Its graph consists of two half lines; such a function is called piecewisely linear.

The modulus function

fulfills the following properties ( are arbitrary real numbers).
  1. .
  2. if and only if .
  3. if and only if or holds.
  4. .
  5. .
  6. For we have .
  7. We have (triangle inequality for the modulus).
  8. .