- #1
mliuzzolino
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Homework Statement
Let A be the set, A = {0, 1, 2, 3}.
Consider the relation R on A give by xRy iff there exists [itex] k \in \mathbb{Z} [/itex] such that x - y = 3k.
Describe the equivalence classes of R.
Homework Equations
The Attempt at a Solution
[itex] E_x = \{y \in A: y - x = 3k, k \in \mathbb{Z} \} [/itex]
For y = 0, k = -x/3
y = 1, k = (1-x)/3
y = 2, k = (2 - x)/3
y = 3, k = (3 - x)/4
Therefore there are four equivalence classes?
I have tried and tried to understand equivalence classes to no avail. I understand the analogies, but then when it transfers to numbers it's just completely lost on me. Even if what I've written above is correct, I just can't wrap my mind around what it means. I'm at one of those points where math makes you feel like the most worthless human to ever live.