- #1

beeftrax

- 9

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"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.