I have a non-symmetric binary relation R over a set X from which I derive the symmetric relation
$$
R'(x,y) : \Leftrightarrow R(x,y) \text{ or } R(y,x)
$$
Is there a common name for this construction?
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Florian Brucker
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I was always fond of the name "Yord". – Asaf Karagila Apr 17 '18 at 09:21
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@AsafKaragila Can you point me to a previous use of your suggestion? I wasn't able to find one. – Florian Brucker Apr 17 '18 at 09:23
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I don't know if there was any. But naming binary relations is kind of like naming kids. Only you get to name them with weird words, without scarring them for life. – Asaf Karagila Apr 17 '18 at 09:25
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@AsafKaragila Well, since there are names for other operations on binary relations, like reflexive closure or transitive closure, I was wondering whether the construction defined above has a similar common name. In that case, using that name would certainly help to communicate my ideas. – Florian Brucker Apr 17 '18 at 09:29
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3Symmetric closure, obviously. – Asaf Karagila Apr 17 '18 at 09:29
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@AsafKaragila . Have you seen the essay, by Carl Sagan, "A Planet Named George"...? – DanielWainfleet Apr 17 '18 at 10:05
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@DanielWainfleet: Nope. – Asaf Karagila Apr 17 '18 at 10:06
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@AsafKaragila . William Hershel discovered Uranus. He claimed that as he was the discoverer, he had the right to name it. He called it George after his patron, the king of England. Naturally the French would have none of this. – DanielWainfleet Apr 17 '18 at 11:04