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    (Original post by wizz_kid)
    AAh ic!

    Physicists Mathematicians are smart lol!
    Corrected.
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    (Original post by yusufu)
    Corrected.
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    (Original post by yusufu)
    Corrected.


    I'm not arguing lol!
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    (Original post by yusufu)
    Corrected.
    Too true, as my maths lecturer said: "Physicists just draw pictures and make stuff up when the maths gets too hard. They just say "well it isn't important""

    :p:
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    Not to be picknickity, but this seems to be exactly the sme topic for a thread a few weeks ago. I remeber posting a link to this problem. Why do people keep regurgitating threads such as:

    why does 0.999.. = 1

    why does blah = jay?
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    (Original post by DeanK2)
    Not to be picknickity, but this seems to be exactly the sme topic for a thread a few weeks ago. I remeber posting a link to this problem. Why do people keep regurgitating threads such as:

    why does 0.999.. = 1

    why does blah = jay?
    Errm.... "why do people keep asking why do questions"?
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    (Original post by Mr M)
    Consider this:

    x = 1 + 2 + 3 + 4 + 5 + 6 + ....

    As x is the sum of positive numbers, it must be positive.

    2x = 2 + 4 + 6 + 8 + 10 + 12 + ....

    x = 2x - x = -1 - 3 - 5 - 7 - 9 + ....
    I don't get where the numbers -1, -3, -5 etc are coming from.
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    (Original post by Swayum)
    I don't get where the numbers -1, -3, -5 etc are coming from.
    Take all the even numbers and subtract all the numbers. You are left with the negatives of the odd numbers
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    Oh I see.
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    Surely if one goes by Cantor's definitions of the sizes of infinite sets, the two sets of 'positive integers' and 'positive even integers' are of "equal size", and so by subtracting 'x' from '2x', as the two have an "equal" number of terms, the one-to-one relationship gives the expected result, after subtraction, of 'x'.
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    The point is it doesn't work. You can look at it in loads of different ways to get different answers, hence the problems when considering infinite sequences which don't behave nicely
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    (Original post by TheUnbeliever)
    I think I'm being dense, sorry.

    x = 1 + 2 + 3 + ...
    2x = 2 + 4 + 6 + ...

    x = 2x - x = (2 - 1) + (4 - 2) + (6 - 3) + ...
    x = 2x - x = 1 + 2 + 3 + ...

    No?
    2x - x = (2-2) -1 ... (you subtract the even numbers from the even numbers.
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    (Original post by DeanK2)
    2x - x = (2-2) -1 ... (you subtract the even numbers from the even numbers.
    Oh, oops. Thanks.
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    (Original post by SimonM)
    The point is it doesn't work. You can look at it in loads of different ways to get different answers, hence the problems when considering infinite sequences which don't behave nicely
    Don't get me wrong, I know divergent infinite sums can behave in strange ways and have multiple results from different perspectives. I'm just being devil's advocate

    Sorry for the thread hijack, though this is a similar problem to the original question in that complications can arise when making dodgy assumptions:
    Let 'a' and 'b' be real numbers, both different from 0. Suppose now that a = b. Then the following is true:
    $$

ab = b^2\\

ab - a^2 = b^2 - a^2\\

a(b - a) = (b+a)(b-a)\\

a=b+a$$
    Since a = b, we have a = 2a, and division by 'a' gives 1 = 2.
    What is wrong with the above proof?
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    (Original post by Brook Taylor)
    What is wrong with the above proof?
    Division by zero
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    b-a
    division by 0
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    beaten to it, again
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    And just one more:
    -2 = -2\\

4 - 6 = 1 - 3\\

4 - 6 + \frac{9}{4} = 1 - 3 + \frac{9}{4}\\

(2 - \frac{3}{2})^2 = (1 - \frac{3}{2})^2\\

2 - \frac{3}{2} = 1 - \frac{3}{2}\\

2 = 1

    Edit: Why do I keep getting indents on the first line each time I use LaTeX?
    • Thread Starter
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    Surely the answer is either 1 or 0 depending on whether \displaystyle n_\infty is even or odd? But isn't \infty neither even nor odd?
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    x^2 = y^2 does not imply x = y.
 
 
 
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