Definition:Error/Also defined as

Error: Also defined as

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

The error $\Delta x$ is an indicator of how much difference there is between $x$ and $x_0$.

Absolute Error

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 $x_0 - x$.

Relative Error

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

$\delta x \approx \dfrac {\Delta x} {x_0}$

where:

$\Delta x$ denotes the absolute error of $x_0$

$\approx$ indicates that the value is but approximate.

This can be particularly useful when the true value $x$ can only be speculated.