Definition:Error

Definition

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

The relative error in $x$ is defined as:

$\dfrac {\size {X - x} } X$

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

The absolute error $\varepsilon$ is the difference between $x$ and a $X$, and can be defined in one of three ways:

$\text {(1)}: \quad$

$\ds \varepsilon$

$:=$

$\ds X - x$

$\text {(2)}: \quad$

$\ds \varepsilon$

$:=$

$\ds x - X$

$\text {(3)}: \quad$

$\ds \varepsilon$

$:=$

$\ds \size {X - x}$

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

Different sources use different conventions.

An error is also, in some branches of mathematics, known as a residual.

Not to be confused with a mistake.