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Homework Help
Calculus and Beyond Homework Help
Proving Uncountability of (0,1): A Puzzling Challenge
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[QUOTE="aaaa202, post: 4500180, member: 294903"] [h2]Homework Statement [/h2] The problem is attached as a picture. [h2]Homework Equations[/h2] ... [h2]The Attempt at a Solution[/h2] I have been trying a lot to prove this without any really fruitful approach. At first I thought that the statement was false, or that you could at least construct a sequence of rationals such that V=(0,1) the following way: Let a1 be a real in (0,1). Since the rationals are dense there exists a rational number b1 such that d(a1,b1)<ε. Let this be the first rational number in the sequence. Now let a2 be another real. Because the rationals are dense there exists a rational b2 such that d(a2,b2)<ε/2 etc. etc. and by successive use of this method I could generate the whole (0,1) with my approach. But this fails because (0,1) is not countable. So I'm open for any other approach to this problem. [/QUOTE]
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Calculus and Beyond Homework Help
Proving Uncountability of (0,1): A Puzzling Challenge
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