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Absolute value
The $\textrm{abs}$ function is used when you need to get the size of a number and you don't care if the number is positive or negative. The absolute value just ignores the sign of a number.
Definition
\[ f(x)=|x|= x \text{ if } x>0 \text{ or } -x \text{ if } x<0 \]
Properties
- Always returns a non-negative number.
- The combination of squaring followed by square-root is equivalent
to the absolute value function:
\[
\sqrt{ x^2 } \equiv |x|.
\]