Equivalence Relations on Integers with a Unique Property

[doggie_Walkes]

This is a question from A consise introduction to pure mathematics (Martin Liebeck)

Hi guys, just stuck on one problem was wondering if someone could lend me hand.

Let ~ be an equivalence relation on all intergers with the property that for all "m" is an element of the set of intergers , we have,

m ~ m +5
and also m ~ m+8

Prove that m~ n for all m, n is an element of intergers.

This is on page 161 of Martin Liebeck's book, number 7.

Im really stuck!

 

[lanedance]

didn't i see this posted a few days ago?

anyways, noinking the solution form those posts, use repeated applications of the equivalence relation to show for any n:
n ~ n+1,

then you're pretty much done, maybe with induction implicit, but it should be reasonably easy to see that any n is equivalent to any m, witr repeated application of the above

 

[Dick]

Hint: can you show m~m+15 and m~m+16? Then you are almost there.