do we have any understanding for the distribution of prime numbers or than their basic definition? we have a way to calculate PARTICULAR primes, but is there a pattern or sequence which could simplify, or rather, encapsulate their representation as some algebraic or differential structure?
>>8457999 hint::::
*hint*
Superior highly composite numbers. hint hint hint
*hint*
>>8457999
The riemann zeta function tells you about the distribution of primes and the riemann hypothesis says they are distributed as randomly as possible.
>>8458397
/thread
this is elementary shit, op. get it together
I'm grading homework right now and I'm honestly a bit frustrated:
(∃x)(∀y)(x = y^2)
where the domain is the reals.
I see this as being translated in two different ways:
>There exists an x for all y such that x = y^2.
which I see as false
vs
>There exists an x for each y such that x = y^2.
which I see as true.
What do you guys think?
>>8457796
It's false, obviously.
What it is saying is essentially something like...
There exists a person X such that for all people Y, X is the mother of Y = there is one person who is everyone's mother.
This is clearly nonsense.
Also, for each = for all. Also, even if the quantifiers changed places it would still be false in the reals because negative numbers aren't squares.
What confuses me is how someone who does not understand basic logic is allowed to grade homework.
T
you need to add : or / to make sense of this.
∀y : ∃x / x= y^2
>>8457808
this
Why does the generalization of topology in metric spaces to topological spaces make sense?
For example, it seems like continuity loses its meaning in arbitrary topological spaces that aren't homeomorphic to metric topologies.
(I'm just a notice and haven't taken courses in real analysis nor topology, but I've read some things about them. Please be gentle.)
>>8457774
>notice
novice
without a metric, continuity becomes a formal property that depends on the topology and just keeps track of open-closed data
but you should think of metric spaces as special cases of topological spaces not the other way around
Watch this meme lecture https://www.youtube.com/watch?v=7G4SqIboeig
Continuity <-> preimage of open sets are open
Suppose I wanted to build a lab from scratch.
The first thing would be to acquire reagents.
However, cavemen didn't have sigma-aldrich, so how would one go about synthesizing basic solvents and basic reagents from scratch?
Let us Brainstorm /sci/!
you look up thing-you-want in lange's handbook, and then synthesize it.
there are these huge books in libraries on synthesizing 'basic' reagents. mostly in chemical journals from the industrial revolution. very basic stuff, but it took cavemen 6000 years :^) to figure out
for instance preperation of ether is rather 'simple' but it is talked about in an almost alchemical way.
>>8457731
Well, here's the thing. I understand that I can use reference books to look up procedures and such, and I'm sure that once the "lab" got to a certain point, I would have to do that unless I want to reinvent the wheel. However, I often see many of these procedures require other reagents that one would have to either already have or have to buy.
I want to know how it's possible to start from a certain place, like say, dig up some dirt in the back yard and isolate stuff, and go from there, or something like the production of urea and then synthesize things from there. You know what I mean?
If we had to restart a chemistry lab from scratch post apocalypse, how would one go about doing it?
>>8457731
To go off your example, the preparation of ether would require ethanol and sulfuric acid.
Ethanol, we could just use basic fermentation to acquire some and separate it by distillation.
How would one make sulfuric acid to do this?
Well, reacting sulfur with oxygen and then carrying out other reactions and such.
Where would one get this sulfur? Could one extract it from the ground? Could they maybe salvage some from car batteries? Etc...
how to the flat earthers reconcile the fact that we can travel AROUND the globe though?
What if the Earth is actually flat, and only appears spherical due to gravitational lensing?
The earth is obviously a torus.
>>8457506
Fuck off >>>/r/edditard
would vegetarians die of hunger if they were no longer allowed to eat cultivated plants and only were allowed to eat the plants in their original natural forms?
>>8457462
>original natural forms
From when? 4000BCE? There are lots of cultivated fruits and vegetables whose wild strains don't exist anymore because of disease
>>8457471
I'm just asking if the wild strains have so little nutritional value that you would be busy eating all day and your digestion couldnt keep up
>>8457462
would meat-eaters die of hunger if they were no longer allowed to eat farmed animals and only were allowed to eat the animals in their original natural forms?
Is computer science saturated?
>>8457425
That table is inaccurate. The highest-paid majors are mathematics majors at $200k starting.
If you study computer science now you'll end up with no job because of third world programmers.
>>8457445
300k if you go for a PhD
the most painful experience in my life was a cystoscopy as a male. the procedure itself hurts a lot and then you piss razor blades for 3 days. I was scared of drinking water.
if a cystoscopy is 5/10 on the pain scale then how much is passing a kidney stone?
>>8457404
Friend of mine passed some kidney stones, after shock wave lithotripsy to break them up, and he claimed it was the worst pain he'd ever felt.
I have never had that experience. However, I've got some titanium screws and plates in my face and waking up after surgery was the worst pain I've ever experienced - much worse than the initial injury that necessitated the surgery.
For the first 12 hours post op it was 'Demerol now pls!' over and over again.
>>8457404
Once I got an infected finger from picking the skin at the side of the nail and the nurse just cut it with a scalpel which didn't hurt as it was so swollen but then tried to squeeze out the black infection, didn't even give me a local anaesthetic. When I said it hurt too much she told me to try to get it out myself. Fucking NHS, easily an 8/10.
>>8457404
What the fuck is that pic?
I don't see the stupid questions thread so here goes.
(0.625)^126 < (2.56)^(-3x)
What the fuck is this problem. I've been sitting with this problem for two days now and I still can't solve it. Here's what I tried to do:
(0.625)^126 < (2.56)^(-3x)
(2.56)^-2(126) < (2.56)^(-3x)
(2.56)^-252 < (2.56)^(-3x)
-252 < -3x
84 > x
and I get the interval (- infinity, 84).
But the solution is apparently (- infinity, 21) and Wolfram Alpha shows that too but I don't understand why. What am I doing wrong?
https://www.wolframalpha.com/input/?i=(0.625)%5E126+%3C+(2.56)%5E(-3x)
2.56^-2 != .625
2.56^(1/2) = .625
When it comes down to checking things like this the last resort is to use a calculator to check each and every step so as to isolate the step where a step was made.
>>8457414
You can also use this method to isolate the region where the wrong step was made.
For very long integrals you can check the first half, then the first quarter, then etc...
>>8457414
Thank you, I can't believe I made such a stupid mistake.
>DUDE LETS JUST ADD MORE METALS XD
nature in charge of originality
>>8457314
10/10 post, but check these repeating integers I have
>>8457399
its not funny anymre, everyone knows the GET Algorithm has already been discovered
>>8457399
Kek and checked.
>Hey man, what if, like, every electron were all just the same electron, dude weed lmao
Physicists will defend this.
>>8457297
>again
We are one oscillation trought field of bosons, but I wouldn't call that electron... And I said it so it can be easily attackable to gain vocabulary.
>>8457297
>accepts some parts of physics while refusing other parts
I will never understand this
What do you think about astronauts?
>>8457294
interesting but demanding job,
one I would not be suited to b/c I'm a spaz
thanks for the gondola image
>>8457313
Thanks for the reply!
>>8457294
i think we take for granted what they do, and act way too shocked when a space shuttle explodes.
Is natural selection the "muh invisible hand" of the biological sciences, an idea that was initially adopted because it just made sense at the time but will be eventually abandoned?
>>8457209
and here we go with gorillaposting again...
Yes.
>>8457209
Nice troll, retard.
Literally everyone knows evolution is true, retard. Stop trolling, retard.
>tfw you realize that cats purr to humans only because all the cats who didn't purr got killed off
why's the universe so cruel, lads?
>>8457170
[citation needed]
>>8457173
this
and it isnt cruel just non-discriminate, evolution also fashioned us to be altruistic so it works both ways
>>8457170
You known that big cats that weren't domesticated still purr, right?
Why does your body feel like a gaping asshole when you are sick? Does your body fighting off infection have to cause pain?
t. ignorant texan
>>8457112
inflammation of body tissues is relevant,
that's why COX inhibitors are used as pain killers
https://en.wikipedia.org/wiki/Cyclooxygenase
there are probably many other things at work as well, maybe someone else will shed some light on them
probably because all the people who felt good when they got sick went out and did things and died
>>8457112
If you don't feel pain, how will you know that you need to vomit? It would cause a risk for choking which is why evolution weeded it out.