- #1

- 986

- 9

## Homework Statement

The only thing I need to do now is show that isometric functions commute. I've shown the 3 properties that prove the the set G of isometric functions is a group.

## Homework Equations

If

*f:Z-->Z*is bijective and preserves distances, then

*f*is isometric.

## The Attempt at a Solution

*f*,

*g*in G and

*n*in Z

--------> |

*f(n) - g(n)*| = |

*f(f(n)) - g(f(n))*| = |

*g(f(n) - g(g(n))*|

--------> ?????????

--------> |

*f(g(n)*-

*g(f(n))*| = 0

-------->

*f(g(n))*=

*g(f(n))*. QED.

Can you give me an oh-so-subtle hint? I just started class this week, so I'm not yet in my proper mindset.