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This is not a homework question since I am out of college for a long time.

I was trying to understand the following that [0,1] /\ Q is not closed in R.

My understanding is that u must take a sequence (since this is a metric space) of the form m/n s.t m < n and create a sequence.

So I was trying to construct sequences like 1/2, 2/3, 3/4 but they seemed to be all ending within [0,1] /\ Q. I am not sure but do I have to take a sum or sth but I am not sure how to prove it.