The intervals of real numbers (−∞;0[ , [0;+∞) constitute equivalence classes on ℝ. True or false?

Question

There is no further information given. My thoughts on this question are if there can be equivalence classes if there is no equivalence relation?

Thank you in advance !

Are you sure there is no equivalence relation given? This question does not make sense then, naturally. — Sarvesh Ravichandran Iyer, Nov 12 '17 at 12:02
I'm guessing that the exercise is to identify that these are a partition, and hence there is an equivalence relation that has these as its equivalence classes. — Theo Bendit, Nov 12 '17 at 12:02

score 1 · Answer 1 · answered Nov 12 '17 at 12:03

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True. You are given a partition of $R$. There is a fundamental relationship between partitions and equivalence relations. The equivalence relation here is that $a$ is related to $b$ if and only if they are in the same set.

answered Nov 12 '17 at 12:03

B. Goddard

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The intervals of real numbers (−∞;0[ , [0;+∞) constitute equivalence classes on ℝ. True or false?

1 Answers1