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To be or not to be...

What is a good mathematical notation of the criterion, that all variables in an equation must all be zero (or whatever value) or all not be zero (or whatever value)?

On the internet I couldn't find anything that would answer my question. Example of what I think it would look like: $$y = f(x, u, i)$$ $$x, u, i \neq 0 \text{ or } x, u, i = 0$$

Hope to hear from you.

Harish Chandra Rajpoot
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Mudimans
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  • You can write $(x,u,i)=(0,0,0)$ or $(x,u,i)\neq(0,0,0)$. In general, if you have $(x_1,…,x_n)\in E^n$ where $0\in E$, you can write $(x_1,…,x_n)=(0,…,0)$ or $(x_1,…,x_n)\neq(0,…,0)$. – K. Makabre Feb 18 '23 at 23:50
  • @DankaMakabre $(x,u,i)=(1,0,0)\neq(0,0,0)$ but these $x,u,i$ do not satisfy the requirements. – David K Feb 18 '23 at 23:52
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    My bad, I understood all zeroes or some non-zero. Then, $x_1,…,x_n\neq0$ seems pretty standard. – K. Makabre Feb 18 '23 at 23:55
  • In some cases, for example multi-indices, you'd use the notation $\vert a \vert = a_1 + \cdots + a_n$. Then your condition would be 'either $\vert a\vert = 0$ or $\vert a\vert > 1$.' – A rural reader Feb 19 '23 at 01:59
  • @DankaMakabre, would you suggest it to be 'Either 1,…, ≠ 0 or 1,…, = 0' – Mudimans Feb 19 '23 at 21:08

1 Answers1

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"Either $x,u,i$ are all zero or none of them is zero."

Alternatively, "Either $x=u=i=0$ or $xui\neq0.$" But I think this is not as clear as simply saying what you mean.

Not everything has to be a notation.

David K
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  • Thanks for your answer, I agree that saying what you mean is clearer. I also like Danka's second answer. – Mudimans Feb 19 '23 at 20:50