So I am taking a logic course and I supposed to write down a couple of math statements using only mathematical logic symbols (the most basic ones but I can use disjunction and there exists). There are statements that require "such that" symbol in my opinion but I am pretty sure that is implied and I am not sure how to proceed . For example, Any two real numbers can divide some one number. I don't have the symbol for divide so I would have to work around that. What I would do is write for all $a,b$, there exists $x$ "such that" there exists $v_1,v_2$ "such that" $x=av_1$ and $x=bv_2$. Is this correct? Do I just ignore the such that and not write it when I use symbols?
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1See here: https://math.stackexchange.com/questions/309506/symbol-for-such-that-not-in-set – John Feb 05 '18 at 15:54
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I sometimes encounter the notation "" for s.t. (France) – nicomezi Feb 05 '18 at 15:56
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1Not a specific symbol. If formalized, the statement will be : $\forall a, b \ \exists x \ \exists v_1, v_2 \ (x=av_1 \land x=b v_2)$. – Mauro ALLEGRANZA Feb 05 '18 at 16:00
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2in semi-formal style, you can use ":" : forall $a,b$, there are $x, v_1, v_2 : x=av_1 \text { and } x=bv_2$. – Mauro ALLEGRANZA Feb 05 '18 at 16:01
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such that is sometimes written with the symbol $\ni$. – amWhy Feb 05 '18 at 16:47