Jump to content

Open formula

From Wikipedia, the free encyclopedia
This is an old revision of this page, as edited by Jochen Burghardt (talk | contribs) at 15:39, 8 September 2019 (Undid revision 914377550 by 109.166.128.100 (talk): unsourced ("the term ... comes from") and confusing (it is not a matter of consideration whther "x" occurs in a sentence; "x associated to the predicate letter")). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

An open formula is a formula that contains at least one free variable.[citation needed] Some educational resources use the term "open sentence",[1][unreliable source?] but this use conflicts with the definition of "sentence" as a formula that does not contain any free variables.

An open formula does not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like true or false.

For example, when reasoning about natural numbers, the formula "x+2 > y" is open, since it contains the free variables x and y. In contrast, the formula "∃y ∀x: x+2 > y" is closed, and has truth value true.

See also

References and notes

  1. ^ http://mathforum.org/library/drmath/view/53280.html


Stub icon

This mathematical logic-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "https://en.wikipedia.org/w/index.php?title=Open_formula&oldid=914644969"