Question

if x is in Q then x can be written as x = q+r where q is in Z and r is 0<= r < 1
let A_r = { x in Q | the rational remainder of x is equal to r}
I need to show that if x is in A_i and x is in A_j then i = j
in other words if x can be written as x = z+n and x = z' + m where z,z' are in Z and n,m are s.t. 0<= m,n < 1 then m = n.

Answer 1

I know this seems trivial. Having said that....I don't know how to show it.

Answer 2

Well, you could show it using the floor function. Are you familiar with that?

Answer 3

btw I don't think I have seen you in a bit KG, nice work on the 99.

Answer 4

I am not.

Answer 5

ok I guess i have seen that but I did not know the name.

Answer 6

Thanks :) I've been busy this past year. Let me see if I can do it without the floor function.

Answer 7

so that would give f(x) = z and f(x) = z'

Answer 8

I know there has to be some easy way...its so trivial lol.

Answer 9

Well with the floor function, you would get that \(z=z'\). So \(x-z=x-z'\). Hence, \(n=m\).

Answer 10

OK i like that:)

Answer 11

ill just define that function, just in case my teacher says he did not show us that function. :)

Answer 12

Probably a good idea.

Answer 13

ty sir

Answer 14

You're welcome.