• Zero equals infinity?
    119 replies, posted
[QUOTE=Nerts;25380292]I don't know what you're doing there, but infinity is a concept, not a value.[/QUOTE] In calculus and other advanced math infinity can be treated as a value in some cases. [QUOTE=taipan;25381538]Actally. 1/0=∞ Fake edit: err 1=0*∞ ???[/QUOTE] Actually anything divided by zero is undefined, not infinity. There's a difference, since undefined basically means we have no idea, vs infinity being an answer (which is incorrect).
lim 1/x = ∞ x->0+ lim 1/x = -∞ x->0-
Sort of only tangentially related but google "TeX the world" or tex the world chrome for a brower plugin that allows you to render tex scripts in your browser (or rehost them as nice .pngs to show with people who don't have the plugin) Makes typing math gr8
[QUOTE=JohnnyMo1;25381216]Rebuttal Part 1: Numbers exist in an objective sense and math is simply a way of describing them Rebuttal Part 2: Based on the laws we've defined for mathematics there are no flaws in it. If you're doin' it right things will come out right.[/QUOTE] Then why are there so many loopholes and paradoxes? Ex. 0.9 repeated = 1, but it still is not exactly one... and 1-2+3-4+5..... = 1/4?
This is what I get for not doing my homework.
So basically he's telling us what weird shit we would end up with if it were possible to divide by zero.
[media]http://www.youtube.com/watch?v=tyjTymcxyKc[/media] 0:50 onwards just happened to me when reading this thread.
[QUOTE=Flubadoo;25381820]Then why are there so many loopholes and paradoxes? Ex. 0.9 repeated = 1[/QUOTE] ?? 0.9+0.9+0.9+0.9=3.6 [QUOTE=Flubadoo;25381820] 1-2+3-4+5..... = 1/4?[/QUOTE] =3
I like it when math is ever over someone's head that they'll instantly disregard math as a credible means for anything more complex than addition. [QUOTE=JohnnyMo1;25380969]What? The limit of a series doesn't have to be 0 for it to converge. 1 + 1/2 + 1/4 + 1/8... = 2. That converges.[/QUOTE] Right. If you take the integral of 1/x from 1 to infinity the result will be infinity. Now if you do the same thing with the function 1/(x^1.0001), it will result with 10,000. What is really weird is that if you take the function 1/x and rotate it around the x axis, you'll get an infinite surface area. But then if you find the volume, it will result in pi. So by intuition you could say that it would be impossible to have enough paint to paint the inside, but then again you could say that you could easily say that you could paint the inside by filling it with pi cubic units of paint. A mathematical paradox.
[QUOTE=BrQ;25380498]sounds like mathematical bullshit you made up because you're the only nerd who understands it[/QUOTE] No. I understand it, it's not made up. But I am looking for fallacies because I probably should.
Aah, limits of limits!
[QUOTE=Flubadoo;25381820]Then why are there so many loopholes and paradoxes? Ex. 0.9 repeated = 1, but it still is not exactly one... and 1-2+3-4+5..... = 1/4?[/QUOTE] Well if you really want, you can say that 1 - 1/∞ = .999... 1/∞ goes to 0 So in that case 1 - 0 = .999... 1 = .999... So it should now make sense as to why we can say that. If it still doesn't, think about thirds. 1/3 is equal to .333... Now you may think that adding three thirds will result in .999... But no it doesn't, adding 3 thirds results in 1. Trust me, your distrust in math is more a lack of knowledge. For the second one, I tested it and kept getting -∞ so I don't know where your answer is coming from. Try pairing up some of the numbers there. (1-2) + (3-4) + (5-6)... -1 + -1 + -1... and all of that will give you -∞. So there is even a intuitive proof for that. I'm guessing the function is miswritten. If you want a better proof. The integral of x - (x+1) from 1 to infinity is going to be -(.5x^2 - .5(x+1)^2). Plug in your values and you're going to get -∞. If you don't know what I'm talking about then learn some calculus.
[QUOTE=Flubadoo;25381820]Then why are there so many loopholes and paradoxes? Ex. 0.9 repeated = 1, but it still is not exactly one... and 1-2+3-4+5..... = 1/4?[/QUOTE] .999... = lim(n->infinity) 1-1/10^n = 1-0 = 1. second is false, the series does not converge.
k = 0.999... 10k = 9.999... 10k-k = 9.999... - 0.999... 9k = 9 k = 1 [editline]13th October 2010[/editline] that's just so simple it's kind of pretty
[QUOTE=conan96;25380259]To zero and beyond! By the way, you lost me at Infinity.[/QUOTE] You got me at hello.
[QUOTE=ThePuska;25382839]k = 0.999... 10k = 9.999... 10k-k = 9.999... - 0.999... 9k = 9 k = 1 [/QUOTE] You rounded. Your faulty math is incorrect. 10k-k would equal 9.9999999... you're right, but the three dots represents ongoing string of digits, ergo you broke the chain of infinity somewhere and rounded the last .999998 (of the product of 10 and .9999....) to .999999 If it was really infinite 9's, you couldn't subtract it. k would still equal 0.9999... This was an interesting one to read, but they are just dumb, yet cool, tricks to make someone think something stupid.
I dislike numbers
[QUOTE=Kill001;25380301]Based on this simple equation (from wiki), actually, the variables can equal infinity too much easier than the one above too[/QUOTE] Yeah! Because breaking rules and making random assumptions to aide you isn't problematic at all.
Well fuck... I'm going to bed.
[QUOTE=GetOutOfBox;25381546]In calculus and other advanced math infinity can be treated as a value in some cases. [/QUOTE] No, see that's where you're wrong. I've gone beyond calc 3, and trust me, you never treat infinity as some value.
[QUOTE=Zer0;25383024]You rounded. Your faulty math is incorrect. 10k-k would equal 9.9999999... you're right, but the three dots represents ongoing string of digits, ergo you broke the chain of infinity somewhere and rounded the last .999998 (of the product of 10 and .9999....) to .999999 If it was really infinite 9's, you couldn't subtract it. k would still equal 0.9999... This was an interesting one to read, but they are just dumb, yet cool, tricks to make someone think something stupid.[/QUOTE] The repeating digits in 10k and k are countably infinite. You can match each repeating digit in 10k to one in k. It's possible and extremely simple to calculate it like that. No one should be rounding anything.
[QUOTE=Zer0;25383024]You rounded. Your faulty math is incorrect. 10k-k would equal 9.9999999... you're right, but the three dots represents ongoing string of digits, ergo you broke the chain of infinity somewhere and rounded the last .999998 (of the product of 10 and .9999....) to .999999 If it was really infinite 9's, you couldn't subtract it. k would still equal 0.9999... This was an interesting one to read, but they are just dumb, yet cool, tricks to make someone think something stupid.[/QUOTE] You aren't thinking enough. I'll lay out some more steps in this to help you understand. k = .999... = 1 - (1/∞) 10k = 10(1 - (1/∞)) = 10 - (10/∞) = 10 - (1/∞) = 9.999... Any constant divided by ∞ will go to 0. This is pretty much stating that (10/∞) and (100000000000000/∞) will both go to 0. Think of it in this way. ∞ and 100000*∞ will both go to ∞. If you don't believe that use common sense. 10k-k = (10 - (1/∞)) - (1 - (1/∞)) = (10 - (1/∞)) + (-1 + (1/∞)) = 10 - 1 - (1/∞) + (1/∞) = 9 What this means is that 9k = 9 k = 9/9 k = 1 This proof is very straightforward and there is no trick to it. You don't know what you're talking about.
[QUOTE=Flubadoo;25381820]Then why are there so many loopholes and paradoxes? Ex. 0.9 repeated = 1, but it still is not exactly one... and 1-2+3-4+5..... = 1/4?[/QUOTE] .9 repeating is exactly one and none of that is a loophole or a paradox except that series thing you posted that's not 1/4 it just diverges. Each term needs to be smaller than the preceding term of an alternating series or else it diverges. [editline]13th October 2010[/editline] [QUOTE=Zer0;25383024]You rounded. Your faulty math is incorrect. 10k-k would equal 9.9999999... you're right, but the three dots represents ongoing string of digits, ergo you broke the chain of infinity somewhere and rounded the last .999998 (of the product of 10 and .9999....) to .999999 If it was really infinite 9's, you couldn't subtract it. k would still equal 0.9999... This was an interesting one to read, but they are just dumb, yet cool, tricks to make someone think something stupid.[/QUOTE] am I really gonna have to pull out the geometric series proof again
Fuck me. And it seems its like saying the alphabet is how easy it is for you.
This is so calculus 1, been there, done that.
[QUOTE=Pepin;25383713]You aren't thinking enough. I'll lay out some more steps in this to help you understand. k = .999... = 1 - (1/∞) 10k = 10(1 - (1/∞)) = 10 - (10/∞) = 10 - (1/∞) = 9.999... Any constant divided by ∞ will go to 0. This is pretty much stating that (10/∞) and (100000000000000/∞) will both go to 0. Think of it in this way. ∞ and 100000*∞ will both go to ∞. If you don't believe that use common sense. 10k-k = (10 - (1/∞)) - (1 - (1/∞)) = (10 - (1/∞)) + (-1 + (1/∞)) = 10 - 1 - (1/∞) + (1/∞) = 9 What this means is that 9k = 9 k = 9/9 k = 1 This proof is very straightforward and there is no trick to it. You don't know what you're talking about.[/QUOTE] That "1/∞" expression is bullshit. This is never used in math. Only by those, who don't know how to deal with infinities. Just the limit [img]http://math.daggeringcats.com/?\lim_{x \rightarrow \infty} \frac{1}{x}[/img] is a valid expression and [b]approaches[/b] zero. The evaluated limit is zero. Anyway, your "0.9999 = 1" proof is similar to this one here: [img]http://math.daggeringcats.com/?x := 0.\overline9[/img] [img]http://math.daggeringcats.com/?\Rightarrow 10 x = 9.\overline9[/img] [img]http://math.daggeringcats.com/?\Rightarrow 10 x - x = 9 x = 9.\overline9 - 0.\overline9 = 9 [/img] divide by 9 [img]http://math.daggeringcats.com/?\Rightarrow x = 1[/img] No magic, paradox or similar stuff used. Just plain math and logic which shows that [img]http://math.daggeringcats.com/? 0.\overline9 = 1[/img].
Oh shit aVoN is here, thread over everyone go home. He is the last word on all things scientific or mathematical on facepunch.
I think you forgot to include yourself as a valuable person too.
I was told by my friend yesterday that because both 1=/=0 and 2=/=0, 1=2. [img]http://dl.dropbox.com/u/6139991/furacepalm.jpg[/img]
Thank you for enlightening me OP.
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