Simple task from Math

Discussion in 'Science' started by 4Runner, Oct 16, 2018.

  1. Dispondent

    Dispondent Well-Known Member Past Donor

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    It doesn't matter how far you go out, whether four digits or 100, you cannot demonstrate it without stopping at some point because otherwise you couldn't end the equation. Wherever you stop to demonstrate, you change the equation. Look at it simply using three digits, 1 x 0.153 = 0.153, whereas if you did the same with 0.999 x 0.153 = 0.1529847. That will happen every single time, no matter how are you go out, you can't demonstrate it without stopping, meaning they are not the same...
     
  2. Mamasaid

    Mamasaid Banned

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    Utterly false. We can demonstrate it by arithmetic proof. You are simply wrong to say this. Similarly, we don't have to perform math for eternity to find the area under a curve, despite calculus being completely reliant on making the approximating quadrilaterals infinitely thin. If what you are saying were true, then we would not have calculus! We would still be doing the arithmetic to arrive at the area under the very fist curve we considered, and we would be doing so forever. Thank goodness what you are saying is false, otherwise we would still be in the post-medieval period, having this discussion on parchment paper delivered by horses and buggies.

    You can't "look at it simply" by using three digits. The arithmetic proof operates on ANY decimal place, be it the third or the three-trillionth. That is the beauty and elegance of the arithmetic proof.

    What will the decimal place be, for ANY decimal place, when adding 0.9999.... and 0.9999...? It will always be 9. Always. I don't have to figure the three-trillionth decimal place, because i already know it will be 9. Do you understand this?

    Also, I think it is important to note something:

    The universe does not care if it "makes sense" to our puny brains, nor is it under any obligation to do so. Just because this doesn't "make sense" to your intuition (thus far supported by false statements and bad mathematics, mind you, and not one example or proof) doesn't make it any less true. Quantum mechanics doesn't make sense to us, but the math checks out.
     
    Last edited: Oct 28, 2018
  3. Dispondent

    Dispondent Well-Known Member Past Donor

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    Except you can't demonstrate it with arithmetic proof, endless chains never end, the equation could never be completed...
     
  4. Mamasaid

    Mamasaid Banned

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    Of course I can. Any math student who has progressed to advanced Calculus or discrete mathematics knows this simple proof,or one of many reiterations of it. In fact,I presented one such example already.

    You can stick to your guns all you like, but you are going to fail the math test.

    The simplest proof involves showing that 3*(1/3)= 1, and showing that any result not equal to 1 is a contradiction of the premises, themselves the definition of the number "1". This is proof by contradiction,a simple method learned in beginning caclulus.

    You keep saying things that are outright false, which should give you pause. What should also give you pause is that you cannot (and will not) produce a single proof or example to support your false claims.

    As it is a well known fact in mathematics that 0.9999...=1, I now will pause my efforts to prove this to you and will let you have the floor. Present a proof, or an example.

    Otherwise...I see no reason to continue to grant you any effort or time.
     
    Last edited: Oct 28, 2018
  5. Mamasaid

    Mamasaid Banned

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    Interestingly, this same phenomenon (rejecting the knowledge and proofs that 0.9999...=1, using intuition and bad arguments) is at the root of "Hoyle's Fallacy", a common fallacy used by those who wish to render the existence of life on Earth "statistically impossible, therefore divine". (I suspect @Dispondent is about to confirm this with his own example)

    By this specious reasoning, the probability of any event can be reduced to zero. Just keep piling on probabilities (the "exactly right" distance from the sun, the "exactly right" climate, the "exactly right" Moon and moon distance, the "exactly right" amount of carbon, nitrogen, an hydrogen, etc.) until you approach a probability of zero.

    The irony of this specious reasoning is two-fold.

    First, there is an implicit acceptance of infinite sums correctly representing reality. This is ironic, as one of the first premises of this bad reasoning is that infinite sums cannot and do not accurately represent reality (just as Zeno claims the arrow can never reach its target). And yet, the peddlers of this fallacy argue that piling on probabilities until they result in zero is acceptable. The "sum" implied is the sum of all such infinite operations.

    Second, each "step" in this fallacy (e.g., considering the small probability of the earth at the "exactly right" distance from the sun) is, itself, an individual example of applying this fallacy. So, the fallacy becomes completely circular, rendering it garbage as a rational argument.

    As a general guide, it is easy to reject this terrible argument, as the arrow always does reach its target. You may use this fallacy to render the probability of a snowflake taking any certain shape to be zero...and yet there it is, a snowflake in that precise shape.

    When a bit of reasoning ends up at any and all events having a zero probability of occuring, we immediately know this reasoning is garbage, and we have known this ever since we discovered the simple idea of calculating infinite sums.
     
    Last edited: Oct 28, 2018
  6. Dispondent

    Dispondent Well-Known Member Past Donor

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    You are wrong, infinite numbers cannot go into calculations and yield answers until infinity has ended, which theoretically isn't possible. Infinity doesn't stop for the arrogance of a few mathematicians...
     
  7. Mamasaid

    Mamasaid Banned

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    Utterly false, as shown by calculus. We can find the area under a hemisphere by approximating it first,using quadrilaterals. We then make these quadrilaterals infinitely thin, resulting in an infinite number of them under the curve. The result of summing them gives the EXACT area under the curve, and doing so takes about 3 minutes, not eternity.

    Enough of your false claims that would net you an "F" on a high school calculus test. Present a mathematical proof, or even an example of getting a different result from an equation by substituting 0.9999... for 1. One example. Just one.

    You will not and cannot. Ever. Not ever.
     
    Last edited: Oct 28, 2018
  8. Dispondent

    Dispondent Well-Known Member Past Donor

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    Not false, if the numbers are infinite the equation never ends, any other ending is not using infinite numbers meaning that the whole premise is thereby false...
     
  9. Mamasaid

    Mamasaid Banned

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    Then why aren't we still trying to calculate the area under a hemisphere, despite calculus deriving this precise answer in minutes?

    Again, where is your proof? Where is your example? Sorry, your intuition fails you.

    I think we are done here. Some people are simply going to fail the math test, despite everyone's best efforts
     
    Last edited: Oct 28, 2018
  10. Dispondent

    Dispondent Well-Known Member Past Donor

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    You want infinity to be a convenient tool that you can turn off and on to make a point, but it doesn't work that way, it is or isn't. If you don't get that, you don't get why you are so wrong on this...
     
  11. Mamasaid

    Mamasaid Banned

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    Excuse you, you mean that, if every mathematician in the world doesn't get it, then....

    Does it not feel absurd to make such a claim, in light of the fact that you are completely incapable of presenting a single proof or example to support your nonsense? It should. Your claim is that you "get it", but mathematicians do not. A rational person would be forced to pause and re-evaluate, in light of this absurd claim.

    Please don't waste my time. Present your proof, or your example.
     
    Last edited: Oct 28, 2018
  12. Dispondent

    Dispondent Well-Known Member Past Donor

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    I showed you an example and you dismissed it because it didn't agree with your false premise...
     
  13. Mamasaid

    Mamasaid Banned

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    You showed no example. Not a single one. No proof, and no example of getting a different result from substituting 0.9999... for 1 in an equation. Any claim to the contrary by you is a lie.
     
  14. Mamasaid

    Mamasaid Banned

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    Incorrect.
     
  15. Mamasaid

    Mamasaid Banned

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    Incorrect. 10*(0.9999...) = 10.
     
  16. Mamasaid

    Mamasaid Banned

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    Wrong. Show us ONE such equation.
     
  17. Mamasaid

    Mamasaid Banned

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    I don't think the engineers who sent the New Horizons probe to Pluto would agree. If their initial trajectory had been off by only 0.000001%, they would have missed Pluto by millions of miles.

    Of course, their trajectory was off by this amount, and they corrected it en route.
     
    Last edited: Oct 28, 2018
  18. WillReadmore

    WillReadmore Well-Known Member

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    The thing is, that % you gave is really a case of counting zeros.

    Engineers definitely count zeros. Powers of 10 tend to be important, while you probably noticed that you gave only 1 nonzero digit - basically a placeholder.

    Engineers accomplished amazing things with slide rules, which are limited to about 3 digits. From there, you need to count zeros.

    Every rocket launch is going to require some amount of correction, as the precise moment of liftoff, air density, winds aloft, etc., aren't known at design time.
     
  19. Mamasaid

    Mamasaid Banned

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    Ah okay , I see what you are saying. Then, fine! I'll put it another way,:

    99.999999% accurate is not good enough.

    Neener neener. :p

    (Just kidding, I get your point)
     
    Last edited: Oct 28, 2018
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  20. Mamasaid

    Mamasaid Banned

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    Another exercise:

    Take a square of area 1 m^2. Cut it into 3 equal parts, using lines.

    What is the area of each equal part? 0.333... m^2.

    Now, put them back together. The area is now 0.999... m^2, right?

    If 0.999... does NOT equal 1, then where did the missing surface area go?
     
    Last edited: Oct 28, 2018
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  21. Mamasaid

    Mamasaid Banned

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    Here is a slightly different proof that I think might more directly address the mental block many people have which prevents them from accepting that 0.999...=1. (Though it will probably just muddy the waters for them, as they still really want to try to count to infinity):

    Prove: 1 - 0.999... = 0.

    Let each decimal place in the solution X to (1 - 0.9999... = X) be represented by integers Xa, where the decimal place of Xa is the place where a= 10^-a, and 'a' belongs to the set of non-negative integers. X0 = the ones place (0.0), X1 = first decimal place (0.0), X2 = second (0.00), and so on. The solution X = X0.X1X2X3...

    X0 = 0, as 1.0 - 0.9 = 0.1.

    Also, X1 = 0, as 0.1 = 0.09 = 0.01 and X2 = 0, as 0.01-.009 = 0.001.

    For any 'a' , [...(Xa)(X[a+1])...] = [...(Xa)(1)(0)...] - [...(Xa)(0)(9)...] = [...(Xa)(0)...]


    So, for any Xa , X(a+1) = 0. And X0 = 0.

    Therefore, for any Xa, Xa = 0.

    Therefore, in the problem 1.000... - 0.999... = X, X = X0.X1X2X3... = 0.000... = 0.
     
    Last edited: Oct 28, 2018
  22. Mamasaid

    Mamasaid Banned

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    Edited for typos and clarity:

    Prove: 1 - 0.999... = 0.

    Let each decimal place in the solution X to (1 - 0.9999... = X) be represented by (integers from 0 to 9) Xa, where the decimal place of Xa is the place where a= 10^-a, and 'a' also belongs to the set of non-negative integers. X0 = the ones place value (X0.0), X1 = first decimal place (0.X1), X2 = second (0.0X2), and so on. The solution X = (X0).(X1)(X2)...

    X0 = 0, as 1.0 - 0.9 = 0.1.

    (Also, X1 = 0, as 0.1 - 0.09 = 0.01, and X2 = 0, as 0.01-.009 = 0.001.)

    For any 'a' , [...(Xa)(X[a+1])...] = [...(Xa)(1)(0)...] - [...(Xa)(0)(9)...] = [...(Xa)(0)...]

    So, for any 'a' , X(a+1) = 0. (And X0 = 0.)

    Therefore, for any 'a', Xa = 0.

    Therefore, in the problem 1.000... - 0.999... = X, X = X0.X1X2X3... = 0.000... = 0.
     
    Last edited: Oct 28, 2018
  23. jay runner

    jay runner Banned

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    For a machinist once you're at the fourth or fifth decimal (depending on the workpiece and specs) the two numbers are the same for all practical purposes.

    But 1.00000000000000 ad infinitum is the decimal that equals the integer 1.
     
    Last edited: Oct 28, 2018
  24. truth and justice

    truth and justice Well-Known Member

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    Reminds me of the reasoning that the length of a line drawn between any two points is infinity (think QM)
     
    Last edited: Oct 31, 2018
  25. Pycckia

    Pycckia Well-Known Member

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    Sure you do.

    .999... + .999... = 1.999... = 2

    But the easiest way to see that 1 =.999... is this:

    if they were not equal you could find a number x so that 1 > x > 0.999...

    Can you find such an x?
     
    Last edited: Oct 31, 2018

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