Thread: Congruence help

Let [a] = {x e Z | x and a are congruent mod m}

This is the exercise:

Describe the set [5] if m = 1. Show that [5] = [-1] in this case.

any IDeas?

Originally Posted by jzellt

Let [a] = {x e Z | x and a are congruent mod m}
Describe the set [5] if m = 1. Show that [5] = [-1] in this case.

To clarify did you mean,



What part are you confused about?

x and a are congruent mod m means the remainder of is the same as the remainder of

Because 5 mod 1 = 0, because (with no remainder) we have,
[5] = {all integers that have a zero remainder when divided by 1} = {all integers} =

Show that [-1] is the set of all integers too.