## Definition Edit

Given a numeric set $\textstyle \mathcal{N}$, the diference distance is a distance function $\textstyle DiffDis: \mathcal{N}\times \mathcal{N}\longrightarrow \mathbb{R}^+$ such that $\textstyle \forall x,y\in \mathcal{N}$

$DiffDis(x,y)=|x-y|.$

## Examples Edit

• $DiffDis(-2,4) = 6$
• $DiffDis(2.5, -1.2) = 3.7$

## Normalization Edit

It is not possible when the range of $\textstyle \mathcal{N}$ is not bounded, otherwise

$DiffSim(x,y)=1-\frac{|x-y|}{\max(\mathcal{N})-\min(\mathcal{N})}.$

## Examples Edit

• If $\textstyle \mathcal{N}=\{0,1,2,\ldots,100\} \quad DiffSim(4,14) = 1-\frac{|4-14|}{100-0} = 0.9$
• If $\textstyle \mathcal{N}=[-10,10] \quad DiffSim(2.5,-1.2) = \frac{|-1.2-2.5|}{10-(-10)} = 0.815$