- #1
Mathematicsresear
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Homework Statement
a relation R⊆ℝ2
It is defined if and only if a2+b2=c2+d2 where (a,b) ∧ (c,d)∈ℝ2
Find all equivalence classes
Homework Equations
The Attempt at a Solution
I said that the following set defines an equivalence class for the above problem:
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[(a,b)] = {(c,d)∈ℝ2 : ((a,b),(c,d))∈R}⊆ℝ2
so I asked myself when is a2+b2=c2+d2 such that (a,b) and (c,d) are elements of the relation and a subset of ℝ2.
I said when d= sqrt(a2+b2-c2) and a2+b2 > c2
I am not sure what to do next.