Mathematics

10:01 PM

I'll surely not pass the examen

@meow-mix What about $A\times B\text{ countable}\implies A,B \text{ countable}$?

If I am asked what kind of modern technology am I going to take with me if I ever get stranded on an isolated island somewhere near the south with no sign of advanced civilization nearby, I am going to take an electric flyswatter (or rather, a mosquitoswatter).

Sylent Nyte

guys, whats the best way of solving an rational inequality such as $\frac{(x+2)(x+1)}{(x+4)(x-4)} > 0$

Kaj Hansen

@BalarkaSen, there probably won't be mosquitoes

meow-mix

@NaCl apply the "Reverse" cantor's diagonal

i.e., show that you can arrange element of $A \times B$ into a diagonal, with length and width countable; that is, $A$ and $B$ are countable

Kaj Hansen

Isolated island = not much food for mosquitoes. There'd need to be a significant animal population and a source of fresh water

PVAL-inactive

10:09 PM

Well if theres no source of fresh water you won't be around long either.

Balarka Sen

Isolated as in isolated from human civilization I meant, I guess.

Kaj Hansen

@PVal, you can get fresh water by desalinating salt water

Sylent Nyte

guys please

Kaj Hansen

Assuming you have some stuff. In this case, you'd just need a small plastic sheet

Oh sorry @Sylent. Let's see

Sylent Nyte

Because I know theres a method where you can use the table of positive and negative however that seems rather tedious

meow-mix

10:11 PM

@NaCl well between every countable set is a bijection to $\mathbb{N}$

Kaj Hansen

@Sylent, that will be positive $\iff$ both the numerator and denominator have the same sign

I think that's the easiest way to do it unfortunately

Balarka Sen

@PVAL Death from dehydration and/or starvation is fine. Death from a million mosquito bites is not.

Kaj Hansen

It's not too bad.

Mike Miller

@PVAL I'm in Texas.

meow-mix

@BalarkaSen i would not want to die by any of those methods

PVAL-inactive

10:12 PM

@Mike Where?

Sylent Nyte

@KajHansen alright thanks

PVAL-inactive

@Kaj I'm not convinced theres a way to effectively desalinate water by hand.

Mike Miller

Dallas. Just the airport though.

Kaj Hansen

Both numerator and denominator are monic quadratics @sylent, and you also have the zeros given to you already. Because they're monic and hence upward-pointing, both are negative only in the interval $\text{first zero} \leq x \leq \text{second zero}$.

PVAL-inactive

Where are you headed?

Mike Miller

10:13 PM

This is the only airport I've seen that's too cheap to offer free WiFi.

Home. I was visiting family in nyc.

Balarka Sen

just watch Bear Grylls I guess

PVAL-inactive

I bet its still better then flying through ORD

ORD is terrible

Kaj Hansen

@PVAL-inactive, dig a hole, fill with salt water, put a cut-in-half coconut shell concave-up inside, cover hole with plastic sheet, put a small amount of pebbles / sand on top to get plastic sheet to form a cone of sorts with vertex inside coconut shell

Salt water evaporates, condenses on plastic sheet, and drips down into coconut shell where it collects as fresh water.

Balarka Sen

maybe I'll dehydrate before making that work tho

Mike Miller

I'be never been or passes through Chicago somehow.

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$Mathematics$ Mathematics