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    1. #101
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      Quote Originally Posted by Xei View Post
      No. They are fractions of whole numbers.
      What?

      2 is a rational number.

      This is 2 in decimal form: 2.

      It terminates. Thus, it is rational.

      Quote Originally Posted by xXSomeGuyXx View Post
      0.999~ doesn't terminate.
      No, but it does repeat.

      -------------

      Look at this:

      2.999... = 3. There are no numbers between those two.

      Again:

      x = 2.9...

      10x = 29.9...

      Subtract the first equation from the second:

      9x = 27

      x = 3

      Therefore, x.999... = x + 1 and .999... = 1.
      Last edited by A Roxxor; 10-24-2008 at 11:49 PM.

    2. #102
      What's up <span class='glow_006400'>[SomeGuy]</span>'s Avatar
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      Right.

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    3. #103
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      All rational numbers can be written as whole number fractions. For example 4/2 = 2. Pi is irrational, and cannot be written as a fraction.

      Quote Originally Posted by xXSomeGuyXx View Post
      Okay, okay, okay.

      I believe .999~ is .999~.

      I believe 1 is 1.
      It doesn't matter what you believe. .99... = 1 and this can be (and has been) proved. Whether or not you believe it doesn't change reality.

    4. #104
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      I'm not a troll. I'm having a debate. Plus, I actually am a nice guy. Trolls suck.

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    5. #105
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      Quote Originally Posted by xXSomeGuyXx View Post
      I'm not a troll.
      You are spouting random crap about a topic you're obviously ignorant about. If that's not trolling that's just plain immaturity.

    6. #106
      Xei
      UnitedKingdom Xei is offline
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      What?

      2 is a rational number.

      This is 2 in decimal form: 2.

      It terminates. Thus, it is rational.
      The definition of a rational number is that it is a fraction of two whole numbers. Decimals have no place in pure maths.

      Your definition includes things like 0.12112211122211112222... which is not rational. In fact it's not even irrational.

    7. #107
      Dream Squirrel Tamias.Squirrel's Avatar
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      You can also see the proof in certain graphs. 1/x-1 for example cannot equal 1, but its value rises or drops indefinitely as it approaches the asymptote. And no matter how close the value gets to 1 (in other words, how many times 9 is repeated), it is never equal to one.

      Asking if .9999999~ repeated is equal to a rational number is like asking the same of infinity. The answer is that it's not a number to begin with, but an irrational system: a term we use to stand for something our minds couldn't normally contend with. Sort of like how we use i to stand for the square root of a -1 (which can't exist, but it's still an essential component of mathematics).
      ~Same squirrel, twice the carbs

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    8. #108
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      Quote Originally Posted by Xei View Post
      The definition of a rational number is that it is a fraction of two whole numbers. Decimals have no place in pure maths.

      Your definition includes things like 0.12112211122211112222... which is not rational. In fact it's not even irrational.
      No, no. I mean repeating. Not patterns. Sorry, wrong word.

      0.12112211122211112222 is irrational, because it doesn't repeat, and it doesn't terminate.

      And yeah, I was just stating the definition I knew. You said "Fractions of whole numbers", which threw me off.

    9. #109
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      Quote Originally Posted by hungrymanz View Post
      You are spouting random crap about a topic you're obviously ignorant about. If that's not trolling that's just plain immaturity.
      Okay, I know absolutely nothing about maths. And I'm not immature. Trolling? Because I believe something else than you do, and am trying to prove it, you think I'm trolling? Yeah, okay. Remind me never to have a debate with you.

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    10. #110
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      Quote Originally Posted by Tamias.Squirrel View Post
      Asking if .9999999~ repeated is equal to a rational number is like asking the same of infinity.
      NO.
      The answer is that it's not a number to begin with, but an irrational system:
      ABSOLUTELY NOT.

      1/3 is clearly a real, rational number. Look at its decimal representation:

      .333....

      IT IS A NUMBER. Irrational system? It is one single number. It doesn't do anything. It is as solid as 2 or 3 or 1/5 or 3/7.

      You can't take a third of a pie and then say that pie's calculating itself out to infinity. You just have a third of a pie. And if you have three thirds, you have one whole, equal to .999... of the pie.

      Remind me never to have a debate with you.
      Fine by me.

    11. #111
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      Quote Originally Posted by xXSomeGuyXx View Post
      0.999~ doesn't terminate.
      Rational numbers either terminate or have repeated decimals.

      Quote Originally Posted by xXSomeGuyXx View Post
      That isn't even close to algebra. That is a numerical expression, not an algebraic expression. ERGO, I do not suck a algebra. Test me. Give me a loong ass algebraic equation and I'll find x for ya.
      Here's a couple that cropped up in my second year astronomy. Good. Fucking. Luck.

      5[exp(x)-1] = x*exp(x)

      and

      (G*M*m) /((r–R)^2) – (G*m*n) /(R^2) = (m*v^2)/(r–R)
      where your goal is to solve for big R as a function of G, M, m, n, v, and r, which can be taken as constants.
      Last edited by drewmandan; 10-25-2008 at 12:02 AM.

    12. #112
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      O_O See ya in a few weeks...lol. Those actually look fun.

      Hey guys, I'm back. Feels good man
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    13. #113
      Dream Squirrel Tamias.Squirrel's Avatar
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      Quote Originally Posted by hungrymanz View Post
      NO.

      You can't take a third of a pie and then say that pie's calculating itself out to infinity. You just have a third of a pie. And if you have three thirds, you have one whole, equal to .999... of the pie.
      That's actually a good point xD Hmm... This is a lot more complicated than I first thought. Maybe we should all just agree that nobody really knows?
      ~Same squirrel, twice the carbs

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    14. #114
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      Lol, sure.

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    15. #115
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      Quote Originally Posted by xXSomeGuyXx View Post
      O_O See ya in a few weeks...lol. Those actually look fun.
      Hint: There's no exact answer for either of them. Kinda blows your mind if you think about that fact.

      EDIT: One thing. The first equation has a trivial solution x=0. I want the non-trivial solution.

      Quote Originally Posted by Tamias.Squirrel View Post
      That's actually a good point xD Hmm... This is a lot more complicated than I first thought. Maybe we should all just agree that nobody really knows?
      No, we do know. It has been proven dozens of different ways, including real number construction, the be-all end-all proof of numbers, that 0.9~ DOES EQUAL 1.

    16. #116
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      Well, yeah., Ima go use a table of solutions.

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    17. #117
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      What about this?

      There are no numbers between 1.000...1 and 1, right?

      So they are the same, because adding the one to the end is redundant.

      So basically, .999... is just 1 - 0.000...1, which is zero, making .999... 1.

    18. #118
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      Quote Originally Posted by drewmandan View Post
      No, we do know. It has been proven dozens of different ways, including real number construction, the be-all end-all proof of numbers, that 0.9~ DOES EQUAL 1.
      He is right. Maybe you don't understand it, Tamias, but there are people who do. I encourage you to keep trying to understand it.

    19. #119
      What's up <span class='glow_006400'>[SomeGuy]</span>'s Avatar
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      Question, exp(x) is to the xth power, correct?

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    20. #120
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      Quote Originally Posted by xXSomeGuyXx View Post
      Question, exp(x) is to the xth power, correct?
      exp(x) is e^x, where e is the usual e

    21. #121
      Dream Squirrel Tamias.Squirrel's Avatar
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      Quote Originally Posted by drewmandan View Post
      No, we do know. It has been proven dozens of different ways, including real number construction, the be-all end-all proof of numbers, that 0.9~ DOES EQUAL 1.
      But it doesn't: Like I said before, the graph 1/x-1 gets infinitely close to 1, but never, ever touches it. The y-values just keep going up or down. So no matter how close to one you 1, you are never exactly on 1.



      I guess I don't get it.
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    22. #122
      Xei
      UnitedKingdom Xei is offline
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      Do you mean 5e^(x+1) = x.e^x ?

      Or 5e^x + 5 = x.e^x?

      Neither of these has solution x=0.

    23. #123
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      Quote Originally Posted by Xei View Post
      Do you mean 5e^(x+1) = x.e^x ?

      Or 5e^x + 5 = x.e^x?

      Neither of these has solution x=0.
      Learn2distribute minus sign

      5[exp(x)-1] = x*exp(x)

      Meaning 5*e^x - 5 = x*e^x, which has a solution x = 0.

      Quote Originally Posted by Tamias.Squirrel View Post
      But it doesn't: Like I said before, the graph 1/x-1 gets infinitely close to 1, but never, ever touches it. The y-values just keep going up or down. So no matter how close to one you 1, you are never exactly on 1.



      I guess I don't get it.
      What is this? Proof by screen shot? Wtf? By the way, 1/(1-x) has nothing to do with the constant number 0.9~. At all.

    24. #124
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      Quote Originally Posted by Tamias.Squirrel View Post
      But it doesn't: Like I said before, the graph 1/x-1 gets infinitely close to 1, but never, ever touches it.
      You have to understand that .999... is a number, not a function or a graph.

    25. #125
      The Anti-Member spockman's Avatar
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      I understand that, hungrymanz.
      What I don't understand is why this thread continues and people still view the issue as debatable despite being shown the 'proof' that they are the same. It is... fact. It's really that simple. Whether or not it makes sense is irrelevant.

      Your logic on the issue is irrevelant.

      Human logic means nothing next to numbers!

      You are all powerless next to the awsome might of calculus! Understand?
      Paul is Dead




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