Symmetric, transitive, not reflexive?

(1) Find a relation that is symmetric and transitive but not reflexive on the integers.

(2) Consider the following “proof” that every symmetric and transitive relation is also reflexive.

Given your answer to the part (1) above, this argument must incorrect. Where was the mistake made?

Let R be a symmetric and transitive relation on a set T. For any a and b

in T, aRb means that bRa because R is symmetric. Furthermore, we can see

that aRa because aRb and bRa and R is transitive. Therefore, aRa and R is

reflexive.

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hi again, is anyone up for another challenge?