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Is it possible to introduce some dimensionalty as $\text{kg}$ for mass or $\text{m}/\text{s}^2$ for mathematical signs: plus - $+$ and minus - $-$.

The main reason of this is to avoid some common mistake related to $\pm$ signs.

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Can you give an example of a mistake that would be prevented? –  Bernhard Nov 15 '12 at 19:28
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up vote 8 down vote accepted

Since $+1$ and $-1$ are multiples of each other and $(+1) + (-1)$ makes perfect sense, these two would have to have the same dimension (and hence would not help avoid confusion) - which in fact already exists, it is the dimensionless "dimension" $1$.

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