Definition:Error/Absolute

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Definition

Let $x_0$ be an approximation to a (true) value $x$.


The absolute error of $x_0$ in $x$ is defined as:

$\Delta x := x_0 - x$


Correction

The correction to $x$ is the quantity that needs to be added to $x_0$ to change it to $x$.

That is, the correction to $x$ is defined as $-\Delta x$.


Also defined as

The absolute error of $x_0$ in $x$ can also be seen defined as:

\(\text {(1)}: \quad\) \(\ds \Delta x\) \(:=\) \(\ds x - x_0\)
\(\text {(2)}: \quad\) \(\ds \Delta x\) \(:=\) \(\ds \size {x_0 - x}\)

where $\size {x_0 - x}$ denotes the absolute value of $x_0 - x$.


Also see

  • Results about errors can be found here.


Sources