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anonymous · Answer

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anonymous · Answer

basically realize that there is always going to be an irrational number between 2 rational numbers and going to be a rational number between 2 irrational number

there will be no limit because the graph is going to keep jumping back and forth between 0 and 1

anonymous · Answer

Is this related to that example where if you drew a number line and plotted all of the rationals as red dots and all of the irrationals as blue dots, then all you would see is blue dots?

anonymous · Answer

if you zoomed in close enough, you would see it alternating between blue and red dots

anonymous · Answer

So there will never be two successive rationals or irrationals?

anonymous · Answer

there might be, but that would be really hard to prove

anonymous · Answer

this is a nice question so *bookmark ... :)

anonymous · Answer

Any ideas on how to start a formal proof? I am trying the contradiction, but not really getting anywhere.

anonymous · Answer

The problem is famous. It has many branched applications in various situations in math. You should not superficially "just get the proof" - it is important chapter in math-analysis.
READ UP on it , it is called THE DIRICHLET FUNCTION

anonymous · Answer

This could help. Thanks @Mikael !

anonymous · Answer

by the way , the solution per-se is NOT complicated

anonymous · Answer

Yes, I realise that reading http://en.wikipedia.org/wiki/Nowhere_continuous_function. Thanks!