I'm reading "A Course in Advanced Calculus" by Robert Borden, and one of the problems begins as follows:(adsbygoogle = window.adsbygoogle || []).push({});

"Prove that the field Q is a lattice, but not a (sigma)-lattice, under the usual order" (pg.25)

Q is of course the rational numbers.

However, Q doesn't seem to be a lattice, since the supremum of, say, [0,1] doesn't exist, since given any upper bound eg 1.1, a smaller upper bound eg 1.01 that is still in Q can be found.

So is Q not in fact a lattice, or am I missing something?

I apologize if this is in the wrong forum.

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# Is Q a lattice?

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