I am having a difficult time trying to give words to an equivalence, namely, $\preceq$; for instance, how would I word $x \preceq y$? I know it's not that x is less than or equal to y, because $\preceq$ is just a generalization of different equivalences.
Equivalence Notation
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$\begingroup$
notation
discrete-mathematics
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2I would not expect to see the symbol $\preceq$ used for an equivalence relation; rather, I’d expect it to be used for a partial order (or one of its generalizations that you probably haven’t encountered yet). – 2012-11-16
1 Answers
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If $\preceq$ is some kind of order (partial or total) you can read $x \preceq y$
as
- $x$ precedes or is equal to $y$
- $x$ is less than or equal to $y$
- $x$ is smaller or equal to $y$
depending on context. Else, you might just read $x$ is in relation with $y$. Note that the code for this is \preceq
which is an abbreviation of "precedes" and "equal".