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[Schilcote]

The rational numbers are countable? Eh, I get confused when different levels(or classifications, or however that works) of infinity come up... I've heard the concept behind that proof before though.

I am sad today because I have clearly gone without studying math for so long that I am excited about rational numbers again.

If you're desperate, you can locate that question I had about capacitors a while back. Might have been in the Happy thread.

[ChairmanPoo]

The ESC issue remains complicated: http://www.ipscell.com/home.php?s=snowballs-chance-that-the-dc-circuit-will-stay-judge-lamberths-ruling

I suppose it's too much to hope that three of the 6 arch-conservative judges will have an ephiphany and rule against Lamberth's stupid verdict....

[Vector]

If you're desperate, you can locate that question I had about capacitors a while back. Might have been in the Happy thread.

Not desperate enough to do applied math, no >_>;;;;  I'm going to get back to work on my Heart of Darkness annotations.  Thanks for the offer, though =)

[Leafsnail]

Oh!  But we know that there must be uncountably many irrational numbers, because the reals are uncountable and the rationals are countable.  Have you seen a proof of that?  It's exceedingly beautiful.

Quick, get thee to Introduction to Real Analysis by Rudin, 3rd edition.  It is most edifying.

Therefore 0% of numbers can be shown with our system.  Therefore no numbers exist, and anyone who thinks otherwise must be insane

Heh, sounds interesting.  Would it involve adding extra numbers to the ends of things endlessly?

[Schilcote]

Yay, everything's working! First try too.

I'm playing it safe by not using the float charger and instead just running down the battery and charging it back up again. I should be able to get... maybe two hours out of this unit? Internal battery is 50,000 mWh... which would be 50 watts, right? At what voltage I don't know... Gonna assume it's 12. So, this battery lasts slightly less than two hours... battery I'm hooked up to is 7 amps @ 12 volts which is 7*12=84 W/h... so I should be good for more than two hours. Unless the laptop's internal battery uses a lower voltage. Gonna use the multimeter as a monitoring system in a second.

EDIT:

According to my calculations, which unlike on TV may or may not be correct, my battery has approximately 10% of it's power left.
Shit.

EDIT:

Okay, no, it's more like 40%. That's still not good.

EDIT:

Uh oh, meter reads 11.15 volts and my screen just flickered. Still, that's about... two hours. Pretty good jurry-rig.
EDIT:

Oh wait, forum time is off... And the battery just failed. So, that's 7:00-6:20... 40 minutes, and I remember putting it to heavy use before without recharging it. Gonna rig up the float charger now.

[Vector]

Heh, sounds interesting.  Would it involve adding extra numbers to the ends of things endlessly?

The first two pieces:

Cantor's Argument for the Rationals
Cantor's Diagonalization Argument for the Reals

The last piece we need is to show that the difference of an uncountable set and a countable one is uncountable.  Because I don't feel like looking it up on the internet, I'll sketch a proof:

The union of two countable sets A, B is countable (if you have f(1) = x, f(2) = y, g(1) = z, g(2) = p and so on, then just construct a function h with domain the natural numbers and range AUB thus: h(n) = f([n+1]/2) (n odd), h(n) = g(n/2) (n even) to get the desired bijection).  The real numbers is the union of the sets of rational and irrational numbers.  Suppose the irrational numbers are countable.  Then the real numbers are the union of two countable sets, contradicting our assumption.

... Hope that was comprehensible ._.

[Acanthus117]

Woaaahhhh

[Mysteriousbluepuppet]

Heh, sounds interesting.  Would it involve adding extra numbers to the ends of things endlessly?

The first two pieces:

Cantor's Argument for the Rationals
Cantor's Diagonalization Argument for the Reals

The last piece we need is to show that the difference of an uncountable set and a countable one is uncountable.  Because I don't feel like looking it up on the internet, I'll sketch a proof:

The union of two countable sets A, B is countable (if you have f(1) = x, f(2) = y, g(1) = z, g(2) = p and so on, then just construct a function h with domain the natural numbers and range AUB thus: h(n) = f([n+1]/2) (n odd), h(n) = g(n/2) (n even) to get the desired bijection).  The real numbers is the union of the sets of rational and irrational numbers.  Suppose the irrational numbers are countable.  Then the real numbers are the union of two countable sets, contradicting our assumption.

... Hope that was comprehensible ._.

i'm doing chemistry in hope of never being obbligated to see these. It made me sad .

[dragnar]

... Hope that was comprehensible ._.

...partially? I'll get back to you on that in a few semesters...

i'm doing chemistry in hope of never being obbligated to see these. It made me sad .

I'm hoping to never take a chemistry course again for similar reasons.

[Vector]

Woaaahhhh

But I restricted myself to one alphabet of the 8 I usually use!  And there isn't even any subscripts, or superscripts, or statements of "the proof follows by abstract nonsense!"

Nah.  I think it's easier to learn this stuff through a textbook.

i'm doing chemistry in hope of never being obbligated to see these. It made me sad .

I feel you, man.  I took the chem majors' intro chem course (I was young and foolish, once) and ... well, that was a bitch.

...partially? I'll get back to you on that in a few semesters...

Haha, looking forward to the conversations.

Now I miss the arguments I used to have with people in elevators as we went to the tenth floor of the math building, the feeling of chalk on your hands and face and in your hair... pfaugh.  Can't get back soon enough.


I am sad because I went back to rewatch the Watchmen movie and have realized just how perturbed I am at its cropped subplots and minced characters.  Suddenly, I have become a fan of this comic book... and I'd never noticed.  And they're making a sequel!  Seriously, guys?  SERIOUSLY?  You want to take that masterpiece, that jewel of human knowledge and craft, and add something?

Pfaugh!  This is why I read bad zombie apocalypse slash fiction--because it adds something to the canon, but it's transient.  We all know it doesn't alter the original, save perhaps the lens through which we see things.  But to staple on something new, something permanent, something we are demanded to accept for purposes of lining some fat man's coffers... no.  Never.  If I can keep from staring at it like a train wreck, I may have to boycott it.

They cannot do this to me :I  I will not allow them to.  If the creator had wanted to write a sequel, I'm sure he would have written it.

He disowned the damned thing.  What does that tell you?  No more sequels, goddammit.  No more bending to the common dollar.  Be something better, corporations of America!  Transcend your greedy purses!

... [/rant]

[Josephus]

Alan Moore disowns everything, so I'm really not surprised.

[Akigagak]

Yeah, Alan Moore would disown himself if he could.

[dragnar]

*rant*

Hey, it could be good. It could make Watchmen as a whole better... It probably almost certainly won't but still, wait til it's out before you despise it. Then chuck tomatoes at the greedy idiots in charge.

[Vector]

*rant*

Hey, it could be good. It could make Watchmen as a whole better... It probably almost certainly won't but still, wait til it's out before you despise it. Then chuck tomatoes at the greedy idiots in charge.

Well, there's been no news out since February of this year.  I may not have to write letters to them when I get out the Angry Penmanship I'm planning to use on the jerks who design superheroine breasts.

Yes, it could be good.  Still, auuuuugh my chest.  And if you think I'm getting a little bit too worked up about something that doesn't even objectively matter: you're right.  All the same, I RAEJed at Disney for stealing fairy tales and certain French novels, and I was royally pissed about the Dragonball live-action movie/whatever--and so Watchmen must get its dues in heart palpitations as well.

The spirit of a thing must be protected.  Just... thank goodness they never tried to sequelify The Little Prince.  I don't know what I'd do.

[Acanthus117]

Heh, Vector, I couldn't comprehend math if I tried.

It's like some newfangled Eldritch language from beyond the universe in a place where Cthulhu's older brother roams, spewing madness and randomness into the stars.

To me, at least.