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Is there a mathematical sign for "or"? When I have to explain something in numbers, and I have two ways to explain it and I need to separate them by a sign.

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The logical "or" is $\vee$; however, unless you are doing mathematical logic like set theory, that symbol is not widely used, because it is usually unnecessary and the work required to understand it outweighs its potential use/time saving.

J. W. Tanner
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