Why is "x is a multiple of y" not Antisymmetric

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x and y are integers

Doesn't it include all (x,x) and is not symmetric?

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If this is a relation on the integers, you have to consider the negative integers, too: $2=(-1)(-2)$, so $2$ is a multiple of $-2$, and $-2=(-1)(2)$, so $-2$ is a multiple of $2$, but $-2\ne 2$.