• Astounding: 1+2+3+4+5+... = -1/12
    123 replies, posted
I shouldn't try to do this while cooking. That last post was dumb. But just because infinity is greater than real numbers, that doesn't conclude that infinity is greater than zero.
[QUOTE=KillerJaguar;43500600]But just because infinity is greater than real numbers, that doesn't conclude that infinity is greater than zero.[/QUOTE] So you agree that infinity is greater than all real numbers? And you agree that zero is a real number? Surely there's a direct implication that infinity is greater than zero?
[QUOTE=BrickInHead;43500591]don't you remember the order of operations?[/QUOTE] How do you feel about this application of this shifting operation? I think Lazore may have been concerned with this kind of issues which may arise from its use. [IMG]http://i.imgur.com/u2WIV3a.png[/IMG]
[QUOTE=KillerJaguar;43500600] But just because infinity is greater than real numbers, that doesn't conclude that infinity is greater than zero.[/QUOTE] Elaborate, please do.
It's literally how infinity is defined. Infinity is greater than any real number. If you picked any real number, infinity would be greater than it. So I picked zero.
[QUOTE=KillerJaguar;43500519]But then why is infinity less than 10 false? 10 > 0 infinity > 0 therefore infinity > 10 But then why does it say 10 > infinity > 0 is false[/QUOTE] infinity > 10 > 0
my mind just got bloooown woooooow
So in summary, this isn't true. You only get this result in an analytical environment, but accepting this result produces contradictions so you can't take it as a tautology.
[QUOTE=Ziks;43503099]So in summary, this isn't true. You only get this result in an analytical environment, but accepting this result produces contradictions so you can't take it as a tautology.[/QUOTE] But it is true
[QUOTE=ManiacKiller;43501242]infinity > 10 > 0[/QUOTE] but the average of the sum of the series of numbers leading to infinity =/= infinity
[QUOTE=Number-41;43497343]Maybe you should just start using your brain instead of instantly being scared away from maths. This whole [URL="http://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/"]"I'm not a maths person" is a western bullshit mentality. [/URL] I admit, maths can be hard, and it can make you feel dumb, but that's just part of it. Everyone assumes that when you see a mathematical expression or some reasoning, you're supposed to get it instantly. That's completely untrue. You work hard on it until you get it, and then you continue. You don't read a maths book like any other book, it's rather some sort of "crawling through it". I'm getting my master's in physics (started with a high school degree that allegedly wasn't even good enough for psychology, math-wise) and I still feel dumb on a regular basis . You just accept it and try to do your best. I'm not saying that everyone is equally talented in maths, it's just that the belief that it's solely talent is not true at all. It's the same with music, you don't get skill for free in either of these fields. Some people get a head start, some don't, with hard work you'll get somewhere (kinda cliché I admit) /rant[/QUOTE] Except I do work hard, I've taken Caluclus three times and it just doesn't click with me, even with all the studying. Its completely halted any shape or form of my dream of going into Game Design. So to be honest, while Math is important. [B]FUCK MATH.[/B]
[QUOTE=KillerJaguar;43500600]I shouldn't try to do this while cooking. That last post was dumb. But just because infinity is greater than real numbers, that doesn't conclude that infinity is greater than zero.[/QUOTE] how can you not grasp this relatively simple concept of infinity
[QUOTE=DeEz;43506030]how can you not grasp this relatively simple concept of infinity[/QUOTE] Because infinity not a simple concept.
Are you saying that zero is not a real number?
facepunch knows better than physicists.
[QUOTE=One Ear Ninja;43507460]facepunch knows better than physicists.[/QUOTE] The practice of Metaphysics is subjective to a degree.
[QUOTE=One Ear Ninja;43507460]facepunch knows better than physicists.[/QUOTE] Are you assuming that people on facepunch are not physicists? Also, people are still missing the point. The limit of ∑i as n approaches infinity is divergent. I proved it here: [IMG]http://i.imgur.com/IIFwGIR.png[/IMG] But it is still true that ζ(-1) = -1/12
[QUOTE=OrDnAs;43505532]But it is true[/QUOTE] If you take it as being true you also have to accept that 1=0, using my proof on the second page.
[QUOTE=Ziks;43507785]If you take it as being true you also have to accept that 1=0, using my proof on the second page.[/QUOTE] Your function is not the zeta function, your function is the one I showed above to diverge.
[QUOTE=Quiet;43507800]Your function is not the zeta function, your function is the one I showed above to diverge.[/QUOTE] But the video claims that exact function evaluates as -1/12 when using infinity as input. That is what I am refuting.
[QUOTE=Ziks;43507818]But the video claims that exact function evaluates to -1/12 when using infinity as input. That is what I am refuting.[/QUOTE] I suppose they are not being quite honest.
[QUOTE=Swilly;43505748]Except I do work hard, I've taken Caluclus three times and it just doesn't click with me, even with all the studying. Its completely halted any shape or form of my dream of going into Game Design. So to be honest, while Math is important. [B]FUCK MATH.[/B][/QUOTE] There's also people who just aren't that good at maths, I don't deny that. My point was that the potential to learn maths is just not as rare as people think it is, and that mentality is really akin to the West and it should just get the fuck out of here. I just tried to stop everyone from pre-emptively doubting their own abilities because something doesn't immediately look familiar to them. I'm sorry to hear that it kept you from your dream, though. Maybe you can focus more on the visual aspect, to still do something game design-related? N.B. there's a great problem with maths education too (although it's much harder to pinpoint). I've seen courses in physics that were thought to biologists and veterinarians, and I can believe that they find it difficult because often there's little room for actual maths. They often skip the inner mechanics that are essential to understanding the material.
[QUOTE=Ziks;43507818]But the video claims that exact function evaluates as -1/12 when using infinity as input. That is what I am refuting.[/QUOTE] Evidence: [img]http://puu.sh/6iuDa.png[/img] This is exactly my definition for S, and I demonstrate that the result given is not true (unless I have made a mistake).
For fucks sake, as has been said before, the way they arrive to this result is a different way of summation (and there are a lot). Different methods give different results. For a divergent series to act as function, it may not be multi-valued. Therefore, a divergent series is not a function in the first place because they methods of working them out give different results, unless you include the method of summation as some sort of parameter that makes the function single-valued again. The whole 3-page argument is therefore pointless because everyone is right, on the condition that they used a summation method (correctly!) that is consistent with convergent series ([URL="http://en.wikipedia.org/wiki/Divergent_series"]i.e. regular, linear and stable[/URL]).
[QUOTE=Number-41;43511542]For fucks sake, as has been said before, the way they arrive to this result is a different way of summation (and there are a lot). Different methods give different results. For a divergent series to act as function, it may not be multi-valued. Therefore, a divergent series is not a function in the first place because they methods of working them out give different results, unless you include the method of summation as some sort of parameter that makes the function single-valued again. The whole 3-page argument is therefore pointless because everyone is right, on the condition that they used a summation method (correctly!) that is consistent with convergent series ([URL="http://en.wikipedia.org/wiki/Divergent_series"]i.e. regular, linear and stable[/URL]).[/QUOTE] I pretty much just wrap it into a function to avoid repetition, inside the function is just the divergent series. If you get a result from an unsound method of summation, but that result leads to a contradiction of basic axioms of mathematics (such as proving 1 is equal to 0), I claim that result isn't true. That's all I'm saying.
You cannot wrap it in a function if you ignore that the order of the terms has an influence on the output, because a function is per definition single-valued. You have to account for that, otherwise no sensible discussion can come out of it. If you do want to make it a function that ignores the order of the terms, then for the input tending to infinity you can just say it is undetermined. Because that's what you call a function that has for a single input multiple outputs.
[QUOTE=Swilly;43505748]Except I do work hard, I've taken Caluclus three times and it just doesn't click with me, even with all the studying. Its completely halted any shape or form of my dream of going into Game Design. So to be honest, while Math is important. [B]FUCK MATH.[/B][/QUOTE] I used to be good at math until I got into stuff like trig. Just hit a wall there.
[QUOTE=shadowray7;43494874]Quick rundown of the proof of S1 = 1/2 1 - S1 = 1 - (1 - 1 + 1 - 1 + ...) = 1 - 1 + 1 - 1 + .... = S1 [b]->[/b] 1 - S1 = S1 1 = 2 * S1 S1 =1/2[/QUOTE] why did everyone rate this dumb? this is literally the proof in the video that's linked within the OP's video.
[QUOTE=Number-41;43512223]You cannot wrap it in a function if you ignore that the order of the terms has an influence on the output, because a function is per definition single-valued. You have to account for that, otherwise no sensible discussion can come out of it. If you do want to make it a function that ignores the order of the terms, then for the input tending to infinity you can just say it is undetermined. Because that's what you call a function that has for a single input multiple outputs.[/QUOTE] I did neglect that when constructing the function, true, although my main concern was avoiding repeating the sum expression many times. Is there an issue with the proof if you substitute S(n) with the definition of S(n) at each instance?
As long as you don't manipulate the order of the terms, I don't think it forms a problem to represent it with S(n) It will become a problem as soon as you replace n with infinity, because using the normal definitions of summations and convergence, it clearly is divergent ("=∞"). From then on you are no longer working in a [URL="http://en.wikipedia.org/wiki/Field_(mathematics)"]field[/URL], but in eh, well [URL="http://en.wikipedia.org/wiki/Extended_real_number_line#Algebraic_properties"]it doesn't have a name[/URL]. Presumably because it doesn't have many applications like groups, rings and whatnot do. I like how the page states that every property seems to hold, but it could be undefined. So far for being a convenient property lol For other summation methods you could find a finite value associated with it, but you are no longer using a normal sum, and so you may not just treat it as if it actually were a normal sum. The essence is that you have to be very careful when doing algebraic manipulations with quantities that aren't clearly defined or are undetermined, or are just not part of the set in which you are working (+∞ and -∞ are not a part of the real numbers set!). In this case it's S(∞) which is the culprit.
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