How to find all the orbits of a permutation defined by a function?

I have a function, where T sends Z-->Z, where T(x)=x+5

The only thing I could think of for defining the orbits were orbits like cyclic subgroups under the operation of T (like for instance <1>={1, 6, 11 ...}

but not only would those orbits be infinite, I don't think they are right.

so does anyone have some sort of help to offer on finding orbits of a function with no parameters?

-jackie

Re: How to find all the orbits of a permutation defined by a function?

Re: How to find all the orbits of a permutation defined by a function?

That seems to make sense I am just wary because I have never seen it with not being strictly numerical values.

And just to make sure we're on the same page, I mean orbits in terms of cycles/equivalence classes in abstract.

And thank you very much for responding!

Re: How to find all the orbits of a permutation defined by a function?

Quote:

Originally Posted by

**jackie213** That seems to make sense I am just wary because I have never seen it with not being strictly numerical values.

And just to make sure we're on the same page, I mean orbits in terms of cycles/equivalence classes in abstract.

And thank you very much for responding!

Yes, I think we're on the same wave length.