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For the example given for the natural numbers, the given function, as of may 26, 2009, (n maps to n/2 or (n-1)/2 depending on parity) is not injective, so it is not clear how it generates a group.
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Therefore I removed the following section from the article here, sice it is a chat, rather than encyclopedic text. And unreferenced, too.
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370:{\displaystyle f(n)={\begin{cases}n/2,&{\mbox{if }}n{\mbox{ is even}}\\(n+1)/2,&{\mbox{if }}n{\mbox{ is odd}}\end{cases}}}
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specified is not one-to-one and hence not invertible, and so it is not clear what 'the group of functions
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Split the natural numbers into the odds and the evens. The function
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Perhaps one should say that the 'universe set' is the real numbers
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783:{\displaystyle f_{2}(x)=(x-1)/2}
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109:and see a list of open tasks.
720:{\displaystyle f_{1}(x)=x/2}
668:{\displaystyle \mathbb {R} }
626:{\displaystyle \mathbb {R} }
601:{\displaystyle \mathbb {N} }
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495:{\displaystyle \mathbb {N} }
414:{\displaystyle \mathbb {N} }
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