Wiki source code of identity
Last modified by Administrator on 2020/08/13 18:56
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1.1 | 1 | h1. Notations of identity |
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| 3 | In mathematics, an identity function, is a function that always returns the same value that was used as its argument. | ||
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| 5 | h3. Description of this symbol | ||
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| 7 | - Identity in [openMath/fns1|http://www.openmath.org/cd/fns1.xhtml#identity], and in [MathML|http://www.w3.org/TR/MathML2/chapter4.html#contm.ident]. | ||
| 8 | - identity in [mathWorld|http://mathworld.wolfram.com/IdentityFunction.html], and in [wikipedia|http://en.wikipedia.org/wiki/Identity_function]. | ||
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| 10 | ---- | ||
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| 12 | h3. Observations of identity | ||
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| 14 | Put your observations here... | ||
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| 16 | h4. German | ||
| 17 | !identity1-de.png|align=right! We find in the property on the right, id ~x~ is the identity element of the monoid of all functions from X to X. | ||
| 18 | It is shown in the German book [lineare Algebra|Census.Bibliography#lineareAlgebra-GerdFischer] in page 37, and it is called 'Identische Abbildung' in German context. | ||
| 19 | [Find the example in google books lik|http://books.google.com.eg/books?id=rUlGDEFCRxkC&lpg=PP1&dq=lineare%20algebra&as_brr=0&hl=en&pg=PA37#v=onepage&q&f=false]. | ||
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| 21 | !identity3-de.png|align=right! | ||
| 22 | Also on the right we find another example which represents the identity function. | ||
| 23 | Find the example in the German book [Mathematik Wirklich Versteheny|Census.Bibliography#MathematikWirklichVerstehen] in page number 207. | ||
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| 25 | \\ | ||
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| 27 | h4. English | ||
| 28 | !identity1-en.png|align=right! In [the calculus book|Census.Bibliography#Calculus-withAnalyticGeometry] we find an identity function is represented in page 432. | ||
| 29 | [Go to the example in google books link|http://books.google.com/books?id=jTmuOwwGDwoC&lpg=PP1&pg=PA432#v=onepage&q&f=false]. | ||
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| 31 | \\ | ||
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| 33 | ---- | ||
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| 35 | h3. Encoding the observations of identity | ||
| 36 | - [See encodings|http://devdemo.activemath.org/mathbridge/tools/symbolpresentation.cmd?order=by+Theory&lang=x-all&fmt=html&clipCoordinate=7&omsource=+%3COMOBJ%3E%0D%0A++++++++++%3COMS+cd%3D%22fns1%22+name%3D%22identity%22+%2F%3E%0D%0A++++++++%3C%2FOMOBJ%3E&submit=View] | ||
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| 38 | - [See encodings|http://devdemo.activemath.org/mathbridge/tools/symbolpresentation.cmd?order=by+Theory&lang=x-all&fmt=html&clipCoordinate=10&omsource=%3COMOBJ%3E%0D%0A++++++++++++%3COMA%3E%0D%0A++++++++++++++%3COMS+name%3D%22eq%22+cd%3D%22relation1%22%2F%3E%0D%0A++++++++++++++%3COMA%3E%0D%0A++++++++++++++++%3COMS+name%3D%22nthdiff%22+cd%3D%22calculus1%22%2F%3E%0D%0A++++++++++++++++%3COMA%3E%0D%0A++++++++++++++++++%3COMS+name%3D%22unary_minus%22+cd%3D%22arith1%22%2F%3E%0D%0A++++++++++++++++++%3COMI%3E1%3C%2FOMI%3E%0D%0A++++++++++++++++%3C%2FOMA%3E%0D%0A++++++++++++++++%3COMA%3E%0D%0A++++++++++++++++++%3COMS+name%3D%22compose%22+cd%3D%22fns1%22%2F%3E%0D%0A++++++++++++++++++%3COMV+name%3D%22f%22+%2F%3E%0D%0A++++++++++++++++++%3COMV+name%3D%22f%22+%2F%3E%0D%0A++++++++++++++++%3C%2FOMA%3E%0D%0A++++++++++++++%3C%2FOMA%3E%0D%0A++++++++++++++%3COMV+name%3D%22id%22+%2F%3E%0D%0A++++++++++++%3C%2FOMA%3E%0D%0A++++++++++%3C%2FOMOBJ%3E&submit=View] | ||
| 39 | - [See encodings|http://devdemo.activemath.org/mathbridge/tools/symbolpresentation.cmd?order=by+Theory&lang=x-all&fmt=html&clipCoordinate=1&omsource=+%3COMOBJ%3E%0D%0A++++++++++++++%3COMA%3E%0D%0A++++++++++++++++%3COMS+cd%3D%22fns1%22+name%3D%22identity%22+%2F%3E%0D%0A++++++++++++++++%3COMV+name%3D%22a%22+%2F%3E%0D%0A++++++++++++++%3C%2FOMA%3E%0D%0A++++++++++++%3C%2FOMOBJ%3E&submit=View] | ||
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| 41 | \\ | ||
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| 43 | ---- | ||
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