I was wondering what Q/Z, or the rational numbers modulo the integers.

[zcdfhn]

I was wondering what Q/Z, or the rational numbers modulo the integers. I am struggling to visualize what the cosets may be.

Thank you for your time.

 

[Hurkyl]

If we represent an element of Q/Z by a rational number, only the fractional part is significant. i.e. -3/4, 1/4, and 5/4 all name the same element of Q/Z.

 

[zcdfhn]

Oh ok i think I get it, so rational numbers that are the same signed fractional distance from an integer are in the same coset of Q/Z?