Definition:Error/Also defined as
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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.