Talk:∨

RFV discussion: May–October 2016

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∨

RFV-sense "(algebra, order theory) join, supremum". Tagged in diff but not listed. Google Scholar is able to find mathematical symbols if you search for their Latex input codes (\vee, \lor), and Google Books almost certainly OCRs this as "v" most of the time, which should help when searching for examples. @Kephir, Msh210, are you familiar with this and if so can you think of collocations / find examples? - -sche (discuss) 04:53, 9 May 2016 (UTC)

I'm almost completely sure this is correct, but I haven't time now to look for cites, I'm afraid. Not a collocation but just another word on the same page can be poset or meet or infimum.​—msh210℠ (talk) 14:32, 9 May 2016 (UTC)

• RFV failed. —Mr. Granger (talk • contribs) 11:50, 12 September 2016 (UTC)

Is this the right sense? I can't tell; I'm not even sure if it's ∨ or v:

• Ecker Peterson, in Proceedings of the Princeton Symposium on Mathematical Programming (Harold William Kuhn):

  Theorum 5A(i). If primal program A is consistent, then it has a finite infimum M_A if, and only if, dual program A is consistent. Proof. [...] Suppose that A and B are both consistent. From Lemma 4B it is clear that v(y) ⪳ M_A ⪳ G₀(x) for each x and y feasible for A and B respectively. [...] Theorum 5A(ii). If dual program B is consistent, then it has a finite supremum M_B if, and only if, primal program A is consistent. [...] Now suppose that A and B are both consistent. From Lemma 4B it is clear that v(y) ⪳ M_B ⪳ G₀(x) for each x and y feasible for A and B respectively. Thus M_B is finite and the proof of Theorem 5A(ii) is complete. [... Next] If primal program A and its dual program B are both consistent, then primal program A has a finite infimum M_A, and dual program B has a finite supremum M_B, with M_A = M_B.

- -sche (discuss) 13:50, 12 September 2016 (UTC)

No, it's a function called v. Lingo Bingo Dingo (talk) 14:14, 12 September 2016 (UTC)

I'm not sure if the symbol is ∨ or ⋁ or another similar symbol, and can't be sure of the sense, but from context this might be the right sense:

• The Case of the Fuzzy Filter Functor, in Applications of Category Theory to Fuzzy Subsets:

  Proposition 4.2. Assume that L is a complete distributive complete lattive. Let X be a set and M,N ∈ L and f,g ∈ L^x with f ∧ g = ᾰ we have M(f) ∧ N(g) = α. If the supremum M ∨ N exists, then for every h ∈ L^x we have (M ⱱ N)(h) = ∨_f∧g=h M(f) ∧ N(g)

- -sche (discuss) 14:03, 12 September 2016 (UTC)

This, OTOH, seems like the right sense:

• 1984, Mathematica Japonicae, volume 29, page 81:
• [...] if and only if (A, ·, 0) is a DLBCK-algebra in which x ∨ y (resp. x ∧ y) is the supremum (resp. infimum) of x and y with respect to the BCK-order.

- -sche (discuss) 14:08, 12 September 2016 (UTC)

Yes, in these examples they are both used as operators. Lingo Bingo Dingo (talk) 14:14, 12 September 2016 (UTC)

Likewise:

• 1967, Set theory (Kazimierz Kuratowski, ‎Andrzej Mostowski), page 150:

  Theorem 3: If φ is a permutation of the set T and the supremum V_t∊T f_t = g exists, then the supremum V_t∊T f_φ(t) also exists and is equal to g (analogously for infimum).

- -sche (discuss) 14:20, 12 September 2016 (UTC)

• 1991, Ralph Henstock, The general theory of integration, page 28:

  if x, y ∊ K, pair (x, y) has a supremum x ∨ y and an infimum x ∧ y.

@Msh210, what do you make of the citations above? google books:"supremum v" and/or google books:"supremum x v" seems to find additional citations. - -sche (discuss) 14:35, 12 September 2016 (UTC)

Cites 1, 2, and 4 use the small symbol between others (∨) and 3 uses the large one to the left of others (⋁). (There are many similar pairs of symbols.) It seems to mean supremum in all four cites.​—msh210℠ (talk) 15:46, 12 September 2016 (UTC)

Those citations look good to me too. —Mr. Granger (talk • contribs) 16:51, 12 September 2016 (UTC)

• RFV passed. —Mr. Granger (talk • contribs) 02:03, 13 October 2016 (UTC)