ah, dense subsets of rationals!

Let Q be the rationals and let Δ_P={A ⊆ P | A is dense in P}. I think I've proved Is it true that for ∀r, ∀f:D_Q→r, ∃D∈Δ_Q such that ∀A∈Δ_D, f(D)=k for some k≤r?

That is, color all the dense subsets of Q with a finite number of colors. Then must there be some dense subset D of Q such that all dense subsets of it have the same color? In fact, I think much more is true but I'm going to check it out first.

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Google Earth via Ryan
A little addicting, I must say...



A thugged out girl tests all of her ring tones as loud as possible for a solid minute.

Preppy girl: Are you serious with that? Can you do everyone a favor and stop?
Thug girl: I know you're not talking to me. You messed with the wrong girl.
Preppy girl: I'm sorry, I can't hear you. Your screaming phone made me deaf.
Thug girl: I'll f her up. But then she'll call the cops; her people love the cops. Go back to where you came from!
Preppy girl: I'm trying to. That's why I'm on the train, you stupid bitch. Look, you got a new cell phone and that's great, but figure it out at home.
Thug girl: I'll f you up. You're f-ing with the wrong girl. Don't be fooled by the pretty face.
Preppy girl: Pretty face? Where?

--N train
from Overheard in New York