JavaScript is required to use Bungie.net

Forums

originally posted in: Infinite series question
Edited by Uncle Putin: 4/3/2013 3:31:58 AM
20
It depends on how you view infinity. If you see infinity as this exact quantity, then it does equal 1. If you view infinity as this never ending number that continuously gets bigger and bigger, then no, it does not equal 1. There are some people out there that would try to argue with you that the series you gave really does equal 1, but I'm not so sure it's true. Let's say there's a marathon going on in your home town. Runner number 74 has this rare condition that allows him to only run half of a distance at a time. So when the race starts, he gets to the halfway mark and then stops. He takes a 2 minute break and then starts running again. However, he gets tired again when he hits the 3/4ths mark, so he waits two minutes and then starts again. However, he gets tired AGAIN and only makes it to the 7/8ths mark. He keeps doing this over and over again into infinity. He never crosses the line because he's always going half of the distance that he needs to. He gets closer and closer, but he never gets there because he's always going half the distance. The same thing applies to your series. The runner is always getting 9/10ths of the way to the finish line, but he just never gets there. I don't know if that helps you, but that's the best I can explain it.
English

Posting in language:

 

Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • Space and numbers are infinitely divisible.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • [quote]It depends on how you view infinity.[/quote] No! [quote]If you see infinity as this exact quantity, then it does equal 1[/quote] ????? [quote]If you view infinity as this never ending number that continuously gets bigger and bigger, then no, it does not equal 1[/quote]???? [quote]There are some people out there that would try to argue with you that the series you gave really does equal 1, but I'm not so sure it's true.[/quote]That series is proof.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • The series is not proof. Just because they put a 1 there does not necessarily mean it's true. I can put a 2 there. Does that prove that it equals 2? No, it doesn't.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • So you're saying the expression is false? Just solve it then. I'd imagine you don't know how to though.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • I'm not saying it's false, I'm just saying that it isn't proving anything. Do you even know what a series means anyway? The very fact that the upper index is infinity tells me that [i]no one[/i] knows how to solve it. The sigma equation does not prove anything, it only proposes something to be true, and it's up to the person to solve it, but for all intents and purposes, you can't solve it because you can't get to infinity.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • Edited by HurtfulTurkey: 4/3/2013 8:42:26 PM
    [quote]The very fact that the upper index is infinity tells me that [i]no one[/i] knows how to solve it.[/quote] [quote]you can't solve it because you can't get to infinity.[/quote] mfw [quote]Do you even know what a series means anyway?[/quote] >Has completed more calculus than 95% of the active users here Here's a simple proof. 1/3 = .3... 2/3 = .6... 3/3 = 1 .3... + .6... = 1 = .9...

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • Now we're getting somewhere. That's an interesting "proof" that I've seen before, but there is a problem with this. YES, .9 repeating acts very very similar to 1, but how do you explain this equation: f(x)=1/x If you graph that equation, the y value in Q1 becomes bigger and bigger the smaller that x gets, However, there is no number that is satisfactory to make the line cross or hit the y axis. Why? Well it should seem obvious. You cannot put a 0 for x because 1/0 is not a real number. The y value is always coming closer and closer to infinity, but it is literally impossible for it to equal that because 1/0 isn't a number.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • [quote]YES, .9 repeating acts very very similar to 1, but how do you explain this equation: f(x)=1/x[/quote] On the y axis, there is an asymptote at 0. This means the y limit of that function is infinity at x = 0. There is also a horizontal asymptote at y = 0. This means that the x limit of the function is infinity at y = 0. [quote]You cannot put a 0 for x because 1/0 is not a real number.[/quote]Why would the fact that it isn't a real number mean I can't graph it? 1/0 is infinity. [quote]The y value is always coming closer and closer to infinity, but it is literally impossible for it to equal that because 1/0 isn't a number.[/quote]No, it is actually infinity. It's not "closer and closer". At the limit of that function, it is infinite. Obviously you can't work with infinity in equations the same way you do with real numbers, but 1/0 is an actual result that is very useful.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • Okay Mr Smart guy, instead of being so high and mighty like you're acting, why don't you be intelligent for a second and try to solve it yourself, that is if you think you're so smart.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • Edited by HurtfulTurkey: 4/3/2013 9:05:41 PM
    Okay. It's Euler's proof: Using the geometric convergence theorem, the result of the series is of the form: a*r/(1-r) Where a = 9, r = (1/10) Therefore the answer is: 9(1/10)/(1-(1/10)) = (9/10)/(9/10) = (.9...)/(.9...) = 1 I'm not being high and mighty. Remember that you're the one that accused me of not even knowing what a series is.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • [quote]Remember that you're the one that accused me of not even knowing what a series is.[/quote] Where is the accusation? I simply asked you if you knew what a series is. I never stated anywhere that you didn't.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • The implication was obvious. Do you still have any questions regarding this subject and the fact that .9 repeating is exactly equal to 1 and that no other interpretation of that statement is correct?

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • Edited by Uncle Putin: 4/3/2013 9:24:49 PM
    The only "implications" that you perceive are that which you create yourself. I didn't want to argue with someone who didn't know what a series is, so that's why I asked. The number .999... implies a series is in play (obviously), and making .999... equal to 1 does not mean it is equal in the normal sense that we are used to. It only implies that the LIMIT of .999... is one because the farther and farther that you go down the line, the closer and closer the series comes to hitting 1, but it doesn't matter how far you go because it will simply never equal 1. All right, let me ask you this. According to you, 1/infinity should equal 0, but why? You can't just erase a value from space and time; it has to go somewhere. The real answer should be a number that's infinitely small, but that still implies that that number has a value to it. We both know that 0 has no value so that simply cannot be true. The answer ACTS a lot like 0, but it is not 0. The number looks like 1*10^infinity, but it still has a value to it since you initially started with a value. Your theorem that you gave is correct, however you are stuck on the fact that the = sign implies a finite relationship between the two numbers. You are treating .999... like it is a number when it is in fact a series as we have already established. You have proven that a series is equal to itself (congratulations). The limit of the series as x approaches infinity is 1, but that does not mean that it [i]does[/i] equal one. Limit {0.999 .... x places} = 1 x-->∞

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • I'm not even sure how to reply to you. I have so far provided several mathematically correct proofs, and you're refusing to believe them. You keep saying things "act" like other things...that is nonsense. You say there is a "normal sense" of equal...that is nonsense. You say a limit does not imply equality...that is nonsense. A limit of a function means that at that x value, the function is exactly equal to that number. [quote]We both know that 0 has no value[/quote]Zero has a value of zero. It does not have "no value". If you're not willing to accept mathematical truths and proofs, I don't know how to explain this to you.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • You're giving me proofs and truths that are indeed very truthful, but you're attributing them to our argument in an incorrect manner. The proof you gave me only showed me that something divided by itself is 1. Congratulations. That does not prove what we're arguing. [quote]Zero has a value of zero. It does not have "no value".[/quote] You're using a circular argument to try to explain something to me. Zero is the absence of value. 1 has value, but 0 does not. 0 is nothing. If you have 1 apple and take it away, you have nothing. That's 0. 0=nothing=no value. It is indeed a number, but it does not have value. I don't understand why you would try to argue this since it's very fundamental. Saying "zero has a value of zero" means that zero is nothing and it has no value, because 0 is the complete absence of value and anything that constitutes it.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • Edited by HurtfulTurkey: 4/3/2013 11:32:18 PM
    Like I said, I don't know what to do to explain this. I've tried showing why I'm authoritative on this subject. I've presented several proofs; you deny them. I'm not attributing them to any argument, they directly prove that .9... = 1. And yes, zero is a value, it equals zero. I really don't understand how I can make any of this clearer. I think you'll just have to wait until calculus to learn it (even though this is simply proven through fractions). .9... equals 1. 1/0 equals infinity. You can take the square root of a negative number. 3 concepts that sound ridiculous but you'll learn eventually.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • You're still wrong. 0 is not a value. It is the absence of value. There is no substance to 0 because there is nothing to give it any value. You keep using circular arguments by saying the value of 0 is 0, which is true but what you just said is that 0 does not have a value because it equals 0, the very thing that has no value. 1-1=0. There is nothing. It has no value. It's nothing. I can't understand why you still think that 0 has any value to it because it doesn't. It's value is 0 which means nothing. But I really need to get a life because I'm arguing with a random person over the internet about trivial math stuff that really doesn't matter at all.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • Edited by HurtfulTurkey: 4/4/2013 4:59:53 AM
    This is definitely not trivial. I urge you to ask your math teacher about this. What do you define as a value? Generally (and mathematically) it's defined as an amount. We know zero is a real number (it's actually an even number too), and we know it is a feasible magnitude. The "absence of value" would be something that isn't a number, like a direction (x, y, etc.). Do you still have any confusion about the fact that .9... = 1?

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • So it really comes down to definitions?

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

  • That's how I've always viewed it. There are different opinions on the matter and I don't know who's right, if there even is a correct answer,but infinity is a strange thing so you can never know for sure. You can only make educated guesses on this, and that's just the conclusion I've come to. But if you see infinity differently than me, then the series might be true.

    Posting in language:

     

    Play nice. Take a minute to review our Code of Conduct before submitting your post. Cancel Edit Create Fireteam Post

You are not allowed to view this content.
;
preload icon
preload icon
preload icon