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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4$\begingroup$ Can you give an example of a mistake that would be prevented? $\endgroup$– BernhardCommented Nov 15, 2012 at 19:28
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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" $1$.
