How to read the tilde in logic?
By John Peck •
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How do you read this? What i think it means is: if and only if $ x_1, y_2 $ are different-than/not $x_2 , y_2 $ then is $$ (x_1)^2 + (y_1)^2 = (x_2)^2 +(y_2)^2 $$
but this makes no sense because to prove that it is an equivalence relation is then it must hold for all the values and i can easily think of a counterexample.
1 Answer
$\begingroup$Note that this is a particular usage of a relation $\sim$ which is not universal or known to everyone, but relies on a definition that you provided in the picture.
Recall that $(x,y)=(a,b)$ is true if $x=a$ and $y=b$.
Similarly, $(x,y)\sim (a,b)$ is true whenever $x^2+y^2=a^2+b^2$.
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