Difference between revisions of "Math equation demo"

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The following shows an angled '''degree''' symbol: <math>\ang{90}^{\circ}</math>
<math>P_{wave} = \frac{\rho g^2 h^2 T_e}{6400 \pi} </math>
<math>\frac{\vec{X}_0}{P(\vec{X}_0)} \nabla_{\{H,T,B,\eta \}} P (\vec{X}_0) = (2, 1, 1, 1) </math>
In more explicit terms, the equaliser consists of an object ''E'' and a morphism ''eq'' : ''E'' → ''X'' satisfying <math>f \circ eq = g \circ eq</math>,
In more explicit terms, the equaliser consists of an object ''E'' and a morphism ''eq'' : ''E'' → ''X'' satisfying <math>f \circ eq = g \circ eq</math>,
and such that, given any object ''O'' and morphism ''m'' : ''O'' → ''X'', if <math>f \circ m = g \circ m</math>, then there exists a [[unique (mathematics)|unique]] morphism ''u'' : ''O'' → ''E'' such that <math>eq \circ u = m</math>.
and such that, given any object ''O'' and morphism ''m'' : ''O'' → ''X'', if <math>f \circ m = g \circ m</math>, then there exists a [[unique (mathematics)|unique]] morphism ''u'' : ''O'' → ''E'' such that <math>eq \circ u = m</math>.




A morphism <math>m:O \rightarrow X</math> is said to '''equalise''' <math>f</math> and <math>g</math> if <math>f \circ m = g \circ m</math>.<ref>{{cite book |last1=Barr |first1=Michael |author-link1=Michael Barr (mathematician) |last2=Wells |first2=Charles |author-link2=Charles Wells (mathematician) |year=1998 |title=Category theory for computing science |page=266 |url=http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf |access-date=2013-07-20 |format=PDF |archive-url=https://web.archive.org/web/20160304031956/http://www.math.mcgill.ca/triples/Barr-Wells-ctcs.pdf |archive-date=2016-03-04 |url-status=dead }}</ref>
The following equation shows how to use square root:
<math> c = \sqrt{a^2 + b^2} </math>
 
 
A morphism <math>m:O \rightarrow X</math> is said to '''equalise''' <math>f</math> and <math>g</math> if <math>f \circ m = g \circ m</math>.

Latest revision as of 09:01, 10 January 2022

The following shows an angled degree symbol:




In more explicit terms, the equaliser consists of an object E and a morphism eq : EX satisfying , and such that, given any object O and morphism m : OX, if , then there exists a unique morphism u : OE such that .


The following equation shows how to use square root:


A morphism is said to equalise and if .