Is this [a] + [b] = [a + b] a well defined operation for this equivalence relation?

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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.

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$$[a] + [b] = [a + b]$$ is not well-defined for example,$$ [2.4]+[3.4]=[2]+[3]=[5]$$

while $$[2.4+3.4]=[5.8]=[6]$$