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A simple geometry question.

Name: Anonymous 2009-04-17 19:33

Are the Reals the convex hull of the Rationals?

Name: Anonymous 2009-04-17 19:40

yes

Name: Anonymous 2009-04-18 6:33

no

Name: Anonymous 2009-04-18 14:48

maybe

Name: Anonymous 2009-04-18 14:48

sometimes

Name: Anonymous 2009-04-18 15:04

Kind of but not really.

Name: Anonymous 2009-04-18 15:08

>>2
>>3
THERE CAN ONLY BE ONE

Name: Anonymous 2009-04-18 16:01

Yes

If we take Q to be a subset of the R-vector space R, The convex hull is the minimal convex subset of R containing Q (going by the definition on wikipedia).  Clearly R is convex and contains Q.  Conversely, if C is the convex hull and x is a real number, then C contains rational numbers a,b such that a < x < b (since C contains Q), and so contains x since C is convex.

Name: Anonymous 2009-04-19 14:53

is that like the hull of a ship, shouldn't a hull be concave or shit would fall out

Name: Anonymous 2009-04-19 15:49

>>9
I guess that would depend on whether you were inside the ship, or outside; eh Pythagoras?

Name: Anonymous 2009-04-20 11:51

THE ANSWER IS ONE

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