x ~ y iff x and y round to the same integer
[a] + [b] = [a + b]
it asks if this is a well-defined operation.
What exactly does this mean? How do I check for it?
Further, what does it mean to add two equivalence classes? (left side of equation)
This is on the real numbers btw.
$$[a] + [b] = [a + b]$$ is not well-defined for example,$$ [2.4]+[3.4]=[2]+[3]=[5]$$
while $$[2.4+3.4]=[5.8]=[6]$$