Wiki source code of right_inverse
Last modified by Administrator on 2020/08/13 18:56
Show last authors
| author | version | line-number | content |
|---|---|---|---|
| 1 | h1. Notations of right_inverse | ||
| 2 | |||
| 3 | Given a map {html}\\(f:S?T\\){html} between sets {html}\\(S\\){html} and {html}\\(T\\){html}, the map {html}\\(g:T?S\\){html} is called a right inverse to {html}\\(f\\){html}, that is, composing {html}\\(f\\){html} with {html}\\(g\\){html} from the right gives the identity on {html}\\(T\\){html}. | ||
| 4 | |||
| 5 | |||
| 6 | h3. Descriptions of this symbol | ||
| 7 | |||
| 8 | - right_inverse in [openMath/fns1|http://www.openmath.org/cd/fns1.xhtml#right_inverse], and it seems it is not in MathML. | ||
| 9 | - right_inverse in [mathWorld|http://mathworld.wolfram.com/RightInverse.html] and in [wikipedia|http://en.wikipedia.org/wiki/Inverse_function#Left_and_right_inverses]. | ||
| 10 | |||
| 11 | ---- | ||
| 12 | |||
| 13 | h3. Observations of right_inverse | ||
| 14 | |||
| 15 | Put your observations here... | ||
| 16 | |||
| 17 | h4. English !right_inverse1-en.png|align=right! | ||
| 18 | As we see in [algebra|Census.Bibliography#Algebra-LaneAndBirkhoff] book, in the example on the right each element !right_inverse2-en.png! has a right inverse !right_inverse3-en.png! . | ||
| 19 | [Go directly to the example in google books links|http://books.google.com/books?id=piwKmqalFswC&lpg=PA48&dq=right%20and%20left%20inverse&lr&pg=PA414#v=onepage&q&f=false]. | ||
| 20 | |||
| 21 | \\ | ||
| 22 | |||
| 23 | ---- | ||
| 24 | |||
| 25 | h3. Encoding the observations of right_inverse | ||
| 26 | [See encodings|http://devdemo.activemath.org/mathbridge/tools/symbolpresentation.cmd?order=by+Theory&lang=x-all&fmt=html&clipCoordinate=0&omsource=%3COMOBJ+xmlns%3D%22http%3A%2F%2Fwww.openmath.org%2FOpenMath%22%3E%0D%0A++%3COMA%3E%0D%0A++++%3COMS+name%3D%22right_inverse%22+cd%3D%22fns1%22+xref%3D%22mbase%3A%2F%2Fopenmath-cds%2Ffns1%2Fright_inverse%22+%2F%3E%0D%0A++++%3COMV+name%3D%22f%22+%2F%3E%0D%0A++++%3COMA%3E%0D%0A++++++%3COMS+name%3D%22right_inverse%22+cd%3D%22fns1%22+xref%3D%22mbase%3A%2F%2Fopenmath-cds%2Ffns1%2Fright_inverse%22+%2F%3E%0D%0A++++++%3COMV+name%3D%22g%22+%2F%3E%0D%0A++++++%3COMV+name%3D%22x%22+%2F%3E%0D%0A++++%3C%2FOMA%3E%0D%0A++%3C%2FOMA%3E%0D%0A%3C%2FOMOBJ%3E&submit=View] | ||
| 27 | |||
| 28 | |||
| 29 | \\ | ||
| 30 | |||
| 31 | ---- |