# Antisymmetric

<mathematics> A relation R is antisymmetric if,

for all x and y,

x R y and y R x

=>

x == y.

I.e. no two different elements are mutually related.

Partial orders and total orders are antisymmetric.

If R is also symmetric, i.e.

x R y

=>

y R x

then

x R y

=>

x == y

I.e. different elements are not related.

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