/sci/ - Science & Math

Kid is an idiot savant, Glen Black is an idiot.

This isn't autism board, it's a science board.

>>6745613
>he can write backwards
HOLY FUCK NEW EINSTEIN

>>6745634
>>6745636
>>6745642
You don't understand. Just look at the moment I said.

>>6745647
Are you talking about "Int Test"? If so see >>6745634

i don't get it.. you think they are telling him how to solve it? or that he looks behind to see if they are paying attention to him?

>>6745660
Prove that a divergent series is convergent...

Which all should be applied in finding a person which is going insane. One flew over the and so on...

>>6745666
dayummm, you are right
http://www.wolframalpha.com/input/?i=sum+of+sin%282*n%29%2F%281%2B%28cosn%29^4%29+from+n%3D1+to+inf

>>6745684
Are you retarded? Anyone could see that either from the partial formula sums or from the increasing fluctuations the integral in the integral test does.

<span class="math">
-1 \leq sin(2n) \leq 1
[/spoiler]
and
<span class="math">
0 \leq cos^{4}(n) \leq 1
[/spoiler]
so it is not convergent but it is bounded:
<span class="math">
-1/2 \leq sin(2n) \leq 1/2
[/spoiler]

First I don't think it's that impressive that a 12 year old is doing calculus II. I learned calculus II when I was 16 and know people who learned it when 14, and I'm sure if we were homeschooled/had parents that pushed us to get moved far beyond our grade level we could have learned it while 12.

Second point is that people that are very advanced at an early age don't always end up being that good at a professional (be it sports, musical, or research) level. A lot of times the support of their parents or their savant-like skill ends up limiting them when it runs out.

Holy shit. Just look at the serious retardation going on in the comment section.

>even the smartest Ant is not smarter than God, neither is the smartest Human
>I bet 100000000$ he ends up an atheist, by age 25.
>I'm tired of having the Big Bang shoved down my throat as "true science." It's a piece of junk, and I realized that from the first time I started studying about it.

>>6745838
You don't get it. His parents got him to memorize every of this shit and write it down on the board to make it like their son is a genius (and collect muh shekels by writing a book on how to raise geniuses).
This is literally child abuse.

What a retard. You can't do an integral test on that series. Just like a parrot. Doesn't understand shit of math.

LOL

>mfw

>>6745844
>Fox News

>>6745684
holy shit. did someone on Fox seriously trolled Dr Barnett? Or were they incapable of asking a correct question?

>>6745844
>I'm tired of having the Big Bang shoved down my throat as "true science." It's a piece of junk, and I realized that from the first time I started studying about it.

The amazing thing about Christians complaining about Muh Secular Creation Event is that originally, the big bang wasn't taken seriously because it seemed too much like some Christian had said "Ok, what if there was nothing, and suddenly there was light?" and it got discarded as dogmatic drivel.

>>6746578
I think someone kinda trolled the kid.
On this serie, root test is inconclusive, ratio test also and integral test can't be used since the function <span class="math">\frac{sin(2n)}{1+cos(n)^4}[/spoiler] is not a positive, monotonic decreasing function. So all the easy tests can't be used to proof the convergence/divergence of this serie. You'd actually have to use your brain to solve this one. Keep in mind that this kid probably learned all his math by heart and doesn't really understand shit of it. That's why he starts using the integral test, which is plain wrong. The one who made this question was a good troll.

>>6746696
How would you solve this? My intuition tells me it converges indefinitely, but I wouldn't know how to prove it.

>>6746725
Could you not just expand it's first few partial sums and show that they diverge?

>>6746747
>>6746725
Are you fucking serious?
The general term of this series doesn't converge toward 0 => therefore the series does not converge.
Simple as that.

>>6746749
Idealy you'd have to prove that. Since n is not real, but natural, it's a bit harder to prove.

>>6745613
>amerifats seriously watch this

holy shit, new definition for trash TV achieved

>>6746835
2n is never equal to pi/2 modulo pi since pi is irrational, thus sin(2n) never equals 0 for all values of n.
1+cos(n)^4 > 1 for all values of n
Therefore sin(2n)/(1+cos(n)^4) != 0 for all values of n.

Not hard at all.

>>6746858
>2n is never equal to pi/2 modulo pi since pi is irrational, thus sin(2n) never equals 0 for all values of n.
*2n is never equal to 0 modulo pi

>>6746845
> 2014
> just now hearing about Fox
https://www.youtube.com/watch?v=kkAngvkWVkk

>>6746858
Just because all terms are nonzero doesn't mean it can't converge to 0... (The series <span class="math">\sum \frac{1}{2^n}[/spoiler] converges) However, you can extract a subsequence which does not converge to 0 since the set <span class="math">\{sin(2n), n \in \mathbb N\}[/spoiler] is dense in [-1,1]

Just because all terms are nonzero doesn't mean it can't converge to 0... (The series 12n converges) However, you can extract a subsequence which does not converge to 0.

>>6746861
my sides have gone back in time

Why do you faggots obsess over jacob barnett.

Goddamnit this is so autistic

I can't actually do any math so is he genius or not? :<

>>6745613
So he memorized a whole bunch of different proofs.
America sure is catching up slowly.

>>6746878
lim sup sin(2n) = 1.
lim inf 1+ cos(n)^4 >= 1

Therefore,
lim sup a_n >= 1
and the series does not converge.

>>6745846
this, actually

A necessary condition for the series to be convergent is, that the sequence <span class="math">\displaystyle \frac{\sin(2n)}{1+\cos^4(n)}[/spoiler] tends to zero as <span class="math"> n \to \infty[/spoiler].
This, however, is not the case as <span class="math">\displaystyle \left|\frac{\sin(2n)}{1+\cos^4(n)} \right|\geq \left|\frac{\sin(2n)}{2}\right|[/spoiler] and <span class="math">\sin(2n)[/spoiler] obviously does not tend to 0.

QED.

PS; I'm Jacob.

>>6746900
He's the biggest piece of scam ever conceived by mankind.
I don't even know how his parents did to get so many journalists to write about how clever this savant idiot is.
Even Wikipedia is being corrupted by his parents.
Just read the discussion, it's cringe worthy.
http://en.wikipedia.org/wiki/Talk:Jacob_Barnett

>>6747003
kek

http://en.wikipedia.org/wiki/Talk:Jacob_Barnett#Addition_of_Unpublished_Manuscripts

>>6745846
Well, did they fake his TED Talk too? I don't think this kid is that special, but I do think he's smart. As for your statement, bullshit. Also, they over-exaggerated the whole thing anyways.

>>6747014
>but I do think he's smart.
It's a smart parrot, yes. But definitely not a genius.

>>6746858
>bla bla bla
>pi is irrational
>bla bla bla
>Not hard at all.

yeah ok, prove it

>>6747058
>>6746987 just did

>>6747011
i cannot stop laughing

>>6747011
holy fucking lol

>>6745846
I doubt he'd be attending college at that age if that was the case.

>>6747097
Note that we don't know much about what he really does, except disproving relativity during his spare time.
Also money can buy everything, even a place at college.

>>6747011
> mfw Wikipedia editors are more autistic than I could have possibly imagined

>>6747102
If it that was the case he wouldn't have been able to graduate.

>>6747011
>When I said that the mathematics made no sense, I didn't mean in the technical sense of being a divergent sum that could be evaluated by nonstandard summation methods. I meant that it makes no sense that anyone educated in mathematics would try to pass this off as research.
9.999...../10

>>6747113
They must constantly be on their guard or they'll be accused of not being objective.

>>6747116
Who cares?
Everything about him screams fake.
I don't even wanna hear what his parents did to get him there in the first place.

>>6747128
I don't doubt that his parents were over hyping him, but I find it vary hard to believe that he is fake.

Like there was that other guy who was solving diff eqs on tv when he was 4 or something.

>>6747140
This video >>6745613
is not doing him any favor...

>look how smart he is! buy the book and your child can be too!
http://www.amazon.com/The-Spark-Mothers-Nurturing-Genius/dp/0812993373/ref=sr_1_1?ie=UTF8&qid=1364871697&sr=8-1&keywords=the+spark+kristine+barnett

>>6747063
pi is irrational because I say so
nice proof there

>>6747063
No I didn't. There is a simple proof(pic related), and many more awesome ones, Hermite's being my favorite one. I think he thought we had to prove π is transcedental which is indeed next to impossible. Stewart's early transcedentals book has a detailed solution which I find pretty nice, but the most famous one is with the Lindemann–Weierstrass theorem, proving the transedesence of e, then π.

With regards, Jacob.

>>6747170
>I googled "proof pi is irrational", copy pasted the first pdf, and called it a proof.
yeah ok, you can't prove it, so not so simple.

>>6747174
Proving Pi being irrational is pretty simple mate. He's right, proving Pi being transcendental is the hard one.

>>6747174
Are you some kind of dense retard?
The proof to the problem asked in OP's video was solved here >>6746987
(which is basically a copy paste from http://math.stackexchange.com/questions/925471/is-sum-n-1-infty-frac-sin2n1-cos4n-convergent))
The proof that pi is irrational is unneeded for this problem and has nothing to do in this thread.

>>6747121
<span class="math">e^{2i\pi}×(10)/10[/spoiler]

>>6747183
Transcentental number to the power of non-transcendental number must be transcendental number.
<span class="math">e^{i\pi}=-1[/spoiler]
>e was proven transcedental
>-1 doesn't seem as much transcendental as e
easy m8

>>6747277
You have to prove that is the case first.

>>6745684
actually it's cos^4(n)
http://www.wolframalpha.com/input/?i=sum+of+sin%282*n%29%2F%281%2B%28cos^4n%29

>that blind use of a random test
lel didnt even think

>>6747300
That isn't even the most concerning thing about it though.
The fact that he didn't check the hypothesis and blind-fully pursued his foolish attempt at proving a false statement are the true problem.
Maybe one day he'll understand that his parents manipulated him.
Maybe he already realized it.

>>6747155

>Kristine Barnett’s son Jacob has an IQ higher than Einstein’s, a photographic memory, and he taught himself calculus in two weeks. At nine he started working on an original theory in astrophysics that experts believe may someday put him in line for a Nobel Prize, and at age twelve he became a paid researcher in quantum physics. But the story of Kristine’s journey with Jake is all the more remarkable because his extraordinary mind was almost lost to autism. At age two, when Jake was diagnosed, Kristine was told he might never be able to tie his own shoes.

More like, how to turn your child into a pretentious twat. If he "learned" calculus in 2 weeks, he clearly hasn't learned much since.

>>6747326
all of this is false m8

>>6746858
Wouldn't call that a proof at all. <span class="math">\sum_1^\infty\frac{1}{n^2}[/spoiler] is never zero for each n, but the serie is obviously convergent. Your argument is invalid.

>>6746987
This reasoning is valid for the reals, but you have to proof it for natural numbers. How could you proof sin(2n) doesn't tend to 0 when n is natural? It's not that simple.

>>6747473
<span class="math">\mathbb{N} \subset \mathbb{R} [/spoiler]

>>6747483
That's not enough.

>>6747473
From the continuity of the sine function, for every e>0 you can choose d bla bla...
For any n, you can pick a number N>n such that |N (mod 2pi) - pi/4| < d. (that means n (mod pi), n an integer, is dense in [0, 2pi])
And then you have that. Just fill in the details, if you want.

>>6747554
Yea I know how epsilon delta works.
>n (mod pi), n an integer, is dense in [0, 2pi]
Exactly, this is what you'd need to proof. Now you have just rewritten the problem in a more specific way. My point is it's not that easy to proof, and of all the ones I've read here, not one was complete:
>>6746749
>>6746858
>>6746903
>>6746987
All these 'proofs' assume n is real. Which it isn't.

>>6747011
10/10

comeday gold

>>6747155
Because autism totally isn't the ultimate wild-card of all mental conditions.

>>6747011

>>6745613
is glenn beck autistic

>>6747473
>How could you proof sin(2n) doesn't tend to 0 when n is natural?

are you literally retarded, kid?
pi/2 multiplied by a natural number is never equal to a natural number because pi is irrational.

Stop shitposting, kid.

haha i like how glenn is still down to earth even though the nerd kid is showing him up. I mean he just takes it like a bro and draws r2d2 like a bawss!

>>6748207
I'll just ignore the swearing... I obviously know what you are trying to say, but it's not that easy. That's not how epsilon delta works.

So you need to proof that <span class="math">\lim_{n\to \infty}\neq 0[/spoiler]
Or, in epsilon delta notation:
<span class="math">(\exists\epsilon>0)(\forall\delta>0)(\exists n\in\mathbb{N})(n>\delta\Rightarrow |sin(2n)|\geq\epsilon)[/spoiler]

As I remarked earlier, when n is real, this is easy to proof, I'll show you:
<span class="math">(\exists\epsilon>0)(\forall\delta>0)(\exists n\in\mathbb{R})(n>\delta\Rightarrow |sin(2n)|\geq\epsilon)[/spoiler]
Choose <span class="math">\epsilon =\frac{1}{2}[/spoiler] Now since <span class="math">\mathbb{R}[/spoiler] is not bounded by <span class="math">\mathbb{N}[/spoiler], we can find, for all <span class="math">2\delta\in\mathbb{R}[/spoiler] a number <span class="math">k\in\mathbb{N}[/spoiler] in order that <span class="math">k>2\delta[/spoiler], now assume k is uneven (if not just add one), then: <span class="math">k>2\delta\Rightarrow \frac{\pi}{2}k>2\delta\Rightarrow \frac{\pi}{4}k>\delta[/spoiler]. Now choose <span class="math">n=\frac{\pi}{4}k[/spoiler], then we get:
<span class="math">n>\delta\Rightarrow |sin(2n)|>\frac{1}{2}[/spoiler], since k is uneven, this becomes:
<span class="math">n>\delta\Rightarrow 1>\frac{1}{2}[/spoiler]
Which is obviously true and concludes the proof.

Now when n is not real, this kind of proof becomes harder. And your remark:
>pi/2 multiplied by a natural number is never equal to a natural number because pi is irrational.
Is irrelevant, it just shows you don't know what you're talking about. If you disagree, prove me wrong by giving an epsilon delta proof of:
<span class="math">(\exists\epsilon>0)(\forall\delta>0)(\exists n\in\mathbb{N})(n>\delta\Rightarrow |sin(2n)|\geq\epsilon)[/spoiler]
While using your useless remark.
>\inb4 'hurr durr retard' without having the balls to proof it.

>>6748663
FACT

a natural number (i.e. an integer that is more positive than 0 , just incase you're so ignorant that you don't even know that) times an irrational number never equals an integer.

therefore 2n never equals an integer multiple of pie for any n larger than 0

and sin 2n does not tend to zero.

If you want to disagree with 100% facts then go ahead, but all you're doing I making yourself look like you have brain damage, LOL

>>6747814
>Exactly, this is what you'd need to proof.
Yeah, that's the hard part, that's why I didn't do it.

>>6749125
That isn't enough.

For a board where everyone claims to have studied analysis with Baby Rudin you people sure don't know what you're talking about.

>>6747814
>All these 'proofs' assume n is real. Which it isn't.
<span class="math">n\in \mathbb{N} \subset \mathbb{R}[/spoiler]

>>6749196
>That isn't enough.

Great argument champ:^)

HES NOT A GENIUS

IM A GENIUS

REIIIIHHHHHHHHHHHHHHH

>>6748663
But this statement is false. You can always choose arbitrarily large integers so that sin(2n) is arbitrarily close to zero. What's needed is that there are some other arbitrarily large integers so that sin(2n) is bounded away from zero.

You can reinterpret the statement in terms of dynamical systems. Let g:S^1 -> S^1 be an irrational rotation. By definition of irrational this means that g^k is never the identity, for any k. Then to show the series doesn't converge we want to show that g^k(1) doesn't converge to 1. But since it's a rotation it is rotationally symmetric, so it suffices to show that g^k doesn't approach the identity, pointwise.

But by now this is clearly absurd. If g^k(x) is epsilon close to x, the only way that g^(k+1)(x) could be epsilon close to x is if g is 2epsilon close to rotation by 2pi. Since this holds for all epsilon it follows that g was the identity to start with.

>>6749496
You probably had to use what he wants you to prove to use what you just did.
There's a simpler way.

Also, I think it's clear he knows about the truth of this claim, he's just asking for a proof, I guess. But /sci/ clearly can't into proof.

>>6747308
He explains himself pretty well, the series converges if and only if the integral of the function converges. Meaning if it diverges the integral will also diverge. Meaning he'd still have to do the integral to test which one is true. Meaning if they let him finish he would have been able to show that it converges.
Guess it doesn't take much to be smarter than 99.99% of the population these days.

>>6749538
>He explains himself pretty well, the series converges if and only if the integral of the function converges.
He attempts to use the integral test on a trig function...a test that requires the function to be monotonic.
>Meaning if they let him finish he would have been able to show that it converges.
It doesn't actually converge though. Its pretty clear from looking at it that the function doesn't even converge to 0 as n->inf

>>6745613

>>6749986
You put philosophy on the wrong end of the spectrum.

>>6749992
>You put philosophy on the wrong end of the spectrum.

No I didn't.

>>6750003
yes you did

>>6750033
>yes you did

Care to explain?

>>6750050
>Philosophy: if A is not true, then I will be sad. Therefore A is true.

>>6750074
>Philosophy: if A is not true, then I will be sad. Therefore A is true.

Woops, that explains it, you poor, poor ignorant person...

"Philosophy is the study of general and fundamental problems, such as those connected with reality, existence, knowledge, values, reason, mind, and language."
http://en.wikipedia.org/wiki/Philosophy

>>6750079
>"Philosophy is the study of general and fundamental problems, such as those connected with reality, existence, knowledge, values, reason, mind, and language."
How does that conflict with what I said? Just because it's a study of something doesn't mean it's rigorous or logical. And philosophy is generally not.

>>6750079

>>6749224
This doesn't matter. In >>6748663 I just showed we can find a real number for every delta so that sin(2n) doesn't converge. A real number is not always a natural number, hence we'll have to proof it seperatly for the natural numbers. The other way around would work, if we can proof it for the natural numbers, it's automatically proved for the reals. Keep in mind it's to proof discontinuity, not continuity.

>>6749496
>What's needed is that there are some other arbitrarily large integers so that sin(2n) is bounded away from zero.
Isn't that what I wrote in epsilon delta, it's the negation of the definition of limit:
><span class="math">(\exists\epsilon>0)(\forall\delta>0 )(\exists n\in\mathbb{N})(n>\delta\Rightarrow |sin(2n)|\geq\epsilon)[/spoiler]
Which statement do you think is false?

>>6749125
Yea that's a fact. However you draw wrong conclusions:
>and sin 2n does not tend to zero.
And what you wrote down there is far from a proof. It's not because a function never becomes zero in it's domain, it can't tend to zero when the argument approaches a point outside it's domain (in this case infinity). I won't waste any time explaining further, just go back to your calculus book pls.

>>6750082
>How does that conflict with what I said?

because you said that philosophy functions on feels... duh.

>>6750094
But it does. And nothing you said conflicts with that.

>>6750086

>>6750097
That doesn't even apply to that comic. Nice try dumbass.

>>6750096
>But it does.

Then explain logic.

>>6749532
Ofc I realise it's not continuous when n is natural. I just pointed out the proof is not that easy, and many people disagreed. None of them provided an 'easy' proof though.

>>6750098
>That doesn't even apply to that comic.

Yes it does.

>>6750099
Why are you asking me to "explain logic"? Isn't that what philosophers are supposed to do. YOU explain logic. I'll wait.

>>6750104
No it doesn't. You haven't addressed the criticism, just showed you are insulted by it. Muh feelings.

>>6750111
>Why are you asking me to "explain logic"? Isn't that what philosophers are supposed to do.

YES, MOTHERFUCKER, YES.
That's my entire fucking point you dense bastard.

>No it doesn't. You haven't addressed the criticism, just showed you are insulted by it. Muh feelings.

My comic was a satirical expose on the nature of comic creator perceptions of truth and fiction, and how the vaunted position as the artist of a cartoon tends to oft create a mental pedestal of pseudo-infallibility and puerile disdain for any opinion that the artist disagrees with.

How EXACTLY does that not apply to your little comic?

>>6750121
>YES, MOTHERFUCKER, YES.
>That's my entire fucking point you dense bastard.
OK, so if that is what philosophy does, please explain logic. I'll wait.

>My comic was a satirical expose on the nature of comic creator perceptions of truth and fiction, and how the vaunted position as the artist of a cartoon tends to oft create a mental pedestal of pseudo-infallibility and puerile disdain for any opinion that the artist disagrees with.
>How EXACTLY does that not apply to your little comic?
I could claim that the nature of you wanting to be right is making you misrepresent the facts and present falsehoods. Do you accept that as a valid counterargument? Does this mean I win the argument? Apparently to you it does. To me it's just a non-sequitur. Argue logically or leave.

>>6750144
>OK, so if that is what philosophy does, please explain logic. I'll wait.

That was 2,000+ years ago, motherfucker.

>I could claim that the nature of you wanting to be right is making you misrepresent the facts and present falsehoods.

noted.

Do you accept that as a valid counterargument?

You mean echoing my argument back at me?
That counterargument?

>Does this mean I win the argument?

It means that you are a parrot.

>Apparently to you it does.

Would you like to explain what you mean, as opposed to mindlessly asserting things with no explanation?


>To me it's just a non-sequitur. Argue logically or leave.

You posted the comic where the artist states that philosophy is based on feels, and used it as proof that philosophy was based on feels, you transparent fuck.

>>6750147
>That was 2,000+ years ago, motherfucker.
So you can't explain logic? That's what I thought.

>Do you accept that as a valid counterargument?
Can't you read? I already said it's a non-sequitur.

>Would you like to explain what you mean, as opposed to mindlessly asserting things with no explanation?
You were arguing that this comic "applies" to my comic, when it doesn't address the argument. I'm confused. Are you now abandoning this argument simply because it's indiscriminant or are you abandoning it because it's irrelevant?

>You posted the comic where the artist states that philosophy is based on feels, and used it as proof that philosophy was based on feels, you transparent fuck.
What are you talking about? When did I use it as proof? Do you not understand the difference between a statement and an argument? Apparently you know nothing about basic philosophy.

They need to just ban philosophy from this bored, any mention of it results in shitposting or arguments.

>>6749986
Nope.

>>6750561
>any mention of it results in shitposting or arguments
So, just like every mention of philosophy ever in any place or time?
>yfw greek forums were just low tech 4chan

>he gives the parents a book on autism

>>6750147
>>6750521

Ok, let's shut this shit down.

Logic is the study of reasoning, it is used in both Math and Philosophy, and could arguably be on this scale, whereas Philosophy could not.

Philosophy is described as: "the most basic beliefs, concepts, and attitudes of an individual or group"
The reason /sci/ doesn't care for Philosophy is that a belief is not rigorous or totally accepted by everyone in a community. A belief can always be refuted and argued against. Mathematical proofs are a set of statements that lead any person that can follow them to understand and accept that a statement is true.

Mathematics is based on a standard set of axioms that although assumed, have not been proven wrong and are accepted by the community as a whole. Hell we can re-write the axioms to make for more interesting outcomes that haven't been seen before. Philosophy has not axioms to follow, no strict rule for sense of self or community, wants and needs, etc.

The reason no one accepts that Philosophy is above Mathematics, or even on the chart, is because it does not deal with verifiable evidence. It is certainly not a higher form of Mathematics as this comic depicts because math is not an applied form of Philosophy. No one can argue with certainty that without Philosophy there cannot be Mathematics, or in other words, that we need Philosophy in order to perform Mathematics.

This argument got too out of hand on both sides

>>6750662
I find that comparing philosophy Against mathematics is something just plain weird, something a woman would do. I am a mathematician.

>>6750701
I do too but the comparison was made and I felt a need to explain and vent. I'm not a fan of philosophy anymore. Although it may be the purest form of whatever mental science class it is in, it shouldn't be compared to these sciences or on the scale of the comic in question.

>>6747011

> pi instead of tau

Epic fail.

>>6747011
I really can't decide how many levels of troll are going on here.

>The paper is troll
>The person who suggested the paper could be troll or retard
>The person calling the paper out as a hoax could be intelligent or troll
>The person defending the paper could be troll or retard

>>6750662
>The reason /sci/ doesn't care
The reason stupid people on /sci/ doesn't care, like you, is that they don't know shit about philosophy.

Pure math is closer to philosophy than it is to science. The acceptance of a set of axioms is a philosophical issue, philosophy deals with every kind of knowledge and was responsible for the creation of math, science and everything else that have to do with reasoning.
Philosophy also deals with religion and subjective values but this is not the same as adopting religions and subjective values.

>>6750701
I'm a mathematician, also, and you're dumb.

> The acceptance of a set of axioms is a philosophical issue, philosophy deals with every kind of knowledge and was responsible for the creation of math, science and everything else that have to do with reasoning.

No, logic is responsible for that. Philosophy is literally pseudo-science.

Convergence of the given function is easily proved using barnetts identity, but i wont bother here since no one would understand.

>plebs

>>6749277
>FACT: 1/n never becomes zero, thus it doesn't tend to 0
That's basically what you claim.
sin(2n) with n being a natural number will never have exactly the same value for two different n (at least not if you use radians). Thus it could be possible that the value of sin(2n) will start at some point to always be less than sin(2(n-1)). So you need to prove that this does not actually happen.
With a bit of thought you might have come to the same conclusion, but not that i expected much from a tripfag.