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An equation doesn't say that two open sentences are equal. Rather, the open sentence is itself (in some cases) an equation. -- Toby 11:54 19 May 2003 (UTC)
I doubt you can find me a mathematician who uses the term "open sentence". I think it's part of the "new math" of the '60s. Good riddance.
Michael Hardy 19:38 23 May 2003 (UTC)
Somewhere on my plans for the future is to write Predicate; I'll work these together somehow then. -- Toby Bartels 06:05 12 Jun 2003 (UTC)
the explanation ought not to limit itself to polynomial equations; the classical examples from logic aren't numerical in nature, and i think today databases are a more obvious application of predicates that deserves to be mentioned as well
Why was Predicate (logic) redirected here? - Chira 02:50, 12 August 2005 (UTC)
Gack. The definition here conflicts strongly with (what I see as) common math usage. It sure would be nice to have some explanation of who uses this mangled terminology, and why. linas ( talk) 17:23, 14 June 2011 (UTC)
Perhaps "open sentence" as it is is a term equivalent to "sentence with (at least)a variable". See the section above.-- 109.166.129.57 ( talk) 23:55, 8 September 2019 (UTC)
I see that an example of closed formula has been given. Other examples derived from it can generated by changing order of quantifiers or of x and y.-- 109.166.130.48 ( talk) 17:36, 15 August 2019 (UTC)
The term "open sentence" is perhaps equivalent to the term "sentence with a variable" x which is free, its domain of values being unspecified.-- 109.166.129.57 ( talk) 23:47, 8 September 2019 (UTC)
I propose that the title of this article be changed into "Open formulae and closed formulae" following the model given by Free variables and bound variables.-- 109.166.129.57 ( talk) 16:45, 9 September 2019 (UTC)
Examples of open or closed formulas can be given when the variables x or y from the formulae Px, Rxy are in fact sequence variables xn, yn like in the case of numerical sequences ( Cullen number, Sierpinski number, Riesel number, etc) where each individual number term of the sequence has a property like being composite or prime for all natural values of the index number n which is present in the generating formula of the sequence. In these cases an infinite sequence of propositions with singular terms are generated and domain of discourse for the sequences variables is also infinite, in connection to an aspect discussed at talk:quantifier (logic)-- 109.166.129.57 ( talk) 02:52, 10 September 2019 (UTC)
I have noticed some examples in the German version of this article de:Freie Variable und gebundene Variable which can be inserted here.-- 109.166.129.57 ( talk) 11:52, 10 September 2019 (UTC)
( Summe endlich vieler Werte) | ist gebunden, und sind frei | |
( Bestimmtes Integral) | ist gebunden, , und sind frei | |
( Grenzwert einer unendlichen Folge) | ist gebunden, ist frei | |
( Grenzwert einer Funktion an der Stelle ) | ist gebunden, und sind frei |
-- 109.166.129.57 ( talk) 11:59, 10 September 2019 (UTC)
Translation
( Sum with a finite number of terms) | is bound, and are free | |
( Definite integral) | is bound, , and are free | |
( Limit of a sequence for infinite sequences) | is bound, is free | |
( Limit of a function for a Function at the value ) | is bound, and are free |
-- 109.166.129.57 ( talk) 12:08, 10 September 2019 (UTC)
Other examples from dewp:
-- 109.166.129.57 ( talk) 12:21, 10 September 2019 (UTC)
I think that the two books from the section "Literatur" of the German article can be inserted here. One of the German mathematician authors has article here.-- 109.166.129.57 ( talk) 12:26, 10 September 2019 (UTC)
I see that a link to predicate variable has been removed by saying that it is not about a variable, but a constant. The reason of removal is weak, the (free or bound) individual variables or the individual constants attached to a predicate letter have the same status due to the equivalence of logical quantifiers to substitution with individual constants (from a domain) in specifying closed formulae (having truth values). The lack of a link to predicate letter does not justify the removal of the link to the existing name predicate variable.-- 178.138.195.100 ( talk) 21:54, 13 June 2021 (UTC)
![]() | This article is rated Start-class on Wikipedia's
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An equation doesn't say that two open sentences are equal. Rather, the open sentence is itself (in some cases) an equation. -- Toby 11:54 19 May 2003 (UTC)
I doubt you can find me a mathematician who uses the term "open sentence". I think it's part of the "new math" of the '60s. Good riddance.
Michael Hardy 19:38 23 May 2003 (UTC)
Somewhere on my plans for the future is to write Predicate; I'll work these together somehow then. -- Toby Bartels 06:05 12 Jun 2003 (UTC)
the explanation ought not to limit itself to polynomial equations; the classical examples from logic aren't numerical in nature, and i think today databases are a more obvious application of predicates that deserves to be mentioned as well
Why was Predicate (logic) redirected here? - Chira 02:50, 12 August 2005 (UTC)
Gack. The definition here conflicts strongly with (what I see as) common math usage. It sure would be nice to have some explanation of who uses this mangled terminology, and why. linas ( talk) 17:23, 14 June 2011 (UTC)
Perhaps "open sentence" as it is is a term equivalent to "sentence with (at least)a variable". See the section above.-- 109.166.129.57 ( talk) 23:55, 8 September 2019 (UTC)
I see that an example of closed formula has been given. Other examples derived from it can generated by changing order of quantifiers or of x and y.-- 109.166.130.48 ( talk) 17:36, 15 August 2019 (UTC)
The term "open sentence" is perhaps equivalent to the term "sentence with a variable" x which is free, its domain of values being unspecified.-- 109.166.129.57 ( talk) 23:47, 8 September 2019 (UTC)
I propose that the title of this article be changed into "Open formulae and closed formulae" following the model given by Free variables and bound variables.-- 109.166.129.57 ( talk) 16:45, 9 September 2019 (UTC)
Examples of open or closed formulas can be given when the variables x or y from the formulae Px, Rxy are in fact sequence variables xn, yn like in the case of numerical sequences ( Cullen number, Sierpinski number, Riesel number, etc) where each individual number term of the sequence has a property like being composite or prime for all natural values of the index number n which is present in the generating formula of the sequence. In these cases an infinite sequence of propositions with singular terms are generated and domain of discourse for the sequences variables is also infinite, in connection to an aspect discussed at talk:quantifier (logic)-- 109.166.129.57 ( talk) 02:52, 10 September 2019 (UTC)
I have noticed some examples in the German version of this article de:Freie Variable und gebundene Variable which can be inserted here.-- 109.166.129.57 ( talk) 11:52, 10 September 2019 (UTC)
( Summe endlich vieler Werte) | ist gebunden, und sind frei | |
( Bestimmtes Integral) | ist gebunden, , und sind frei | |
( Grenzwert einer unendlichen Folge) | ist gebunden, ist frei | |
( Grenzwert einer Funktion an der Stelle ) | ist gebunden, und sind frei |
-- 109.166.129.57 ( talk) 11:59, 10 September 2019 (UTC)
Translation
( Sum with a finite number of terms) | is bound, and are free | |
( Definite integral) | is bound, , and are free | |
( Limit of a sequence for infinite sequences) | is bound, is free | |
( Limit of a function for a Function at the value ) | is bound, and are free |
-- 109.166.129.57 ( talk) 12:08, 10 September 2019 (UTC)
Other examples from dewp:
-- 109.166.129.57 ( talk) 12:21, 10 September 2019 (UTC)
I think that the two books from the section "Literatur" of the German article can be inserted here. One of the German mathematician authors has article here.-- 109.166.129.57 ( talk) 12:26, 10 September 2019 (UTC)
I see that a link to predicate variable has been removed by saying that it is not about a variable, but a constant. The reason of removal is weak, the (free or bound) individual variables or the individual constants attached to a predicate letter have the same status due to the equivalence of logical quantifiers to substitution with individual constants (from a domain) in specifying closed formulae (having truth values). The lack of a link to predicate letter does not justify the removal of the link to the existing name predicate variable.-- 178.138.195.100 ( talk) 21:54, 13 June 2021 (UTC)