Spherical law of cosines: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>YohanN7
CE: inline math->HTML
 
Line 1: Line 1:
The '''extension''' of a [[predicate (mathematics)|predicate]]{{spaced ndash}}a [[truth-value]]d [[function (mathematics)|function]]{{spaced ndash}}is the [[Set (mathematics)|set]] of [[tuple]]s of values that, used as arguments, satisfy the predicate. Such a set of tuples is a [[relation (mathematics)|relation]].
Nice to satisfy you, I am Marvella Shryock. Doing [http://www.wechealthunit.org/sexual-health/stis/resources/curable-and-non-curable-stis ceramics] is what her family members and her enjoy. Puerto Rico is where he's over the [http://www.hamcass.org/index.php?document_srl=268708&mid=gido www.hamcass.org] counter std test always been [http://www.aahealth.org/programs/comm-diseases/hiv-aids/hotlines residing]  [http://xrambo.com/blog/191590 at home std testing] but she needs to move simply because of her family members.  std testing at home He utilized to be unemployed but  std testing at home now he is a pc operator but his marketing never arrives.<br><br>Here is my site - [http://change-university.com/groups/curing-your-yeast-infection-how-to-accomplish-it-easily/ http://change-university.com]
 
For example the statement "''d2'' is the weekday following ''d1''"
can be seen as a truth function associating to each tuple (''d2'', ''d1'')
the value ''true'' or ''false''. The extension of this truth function
is, by convention, the set of all such tuples associated with the
value ''true'', i.e.
 
  {(Monday, Sunday),
  (Tuesday, Monday),
  (Wednesday, Tuesday),
  (Thursday, Wednesday),
  (Friday, Thursday),
  (Saturday, Friday),
  (Sunday, Saturday)}
 
By examining this extension we can conclude that "Tuesday is the weekday following Saturday" (for example) is false.
 
Using [[set-builder notation]], the extension of the [[n-ary|''n''-ary]] predicate <math>\Phi</math> can be written as
:<math>\{ (x_1,...,x_n) \mid \Phi(x_1,...,x_n) \}\,.</math>
 
==Relationship with characteristic function==
If the values 0 and 1 in the range of a [[Indicator function|characteristic function]] are identified with the values false and true, respectively{{spaced ndash}}making the characteristic function a predicate{{spaced ndash}}, then for all relations ''R'' and predicates <math>\Phi</math> the following two statements are equivalent:
*<math>\Phi</math> is the characteristic function of ''R'';
*''R'' is the extension of <math>\Phi</math>.
 
== See also ==
 
* [[Extensionality]]
* [[Intension]]
 
[[Category:Predicate logic]]
 
 
{{logic-stub}}
{{mathlogic-stub}}

Latest revision as of 09:06, 14 December 2014

Nice to satisfy you, I am Marvella Shryock. Doing ceramics is what her family members and her enjoy. Puerto Rico is where he's over the www.hamcass.org counter std test always been residing at home std testing but she needs to move simply because of her family members. std testing at home He utilized to be unemployed but std testing at home now he is a pc operator but his marketing never arrives.

Here is my site - http://change-university.com

Retrieved from "https://en.formulasearchengine.com/index.php?title=Spherical_law_of_cosines&oldid=246448"