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Math Help - Just for fun

  1. #1
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    Just for fun

    I saw this somewhere but I can't remember the reason behind it.

    1/3 + 1/3 + 1/3 = 1

    1/3 = 0.333333333... recurring

    but then

    0.333333 + 0.333333 + 0.3333333 = 0.999999999...
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  2. #2
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    Quote Originally Posted by helpwithassgn View Post
    I saw this somewhere but I can't remember the reason behind it.

    1/3 + 1/3 + 1/3 = 1

    1/3 = 0.333333333... recurring

    but then

    0.333333 + 0.333333 + 0.3333333 = 0.999999999...
    Well, one can express 0.99999 (repeating) as the limit as x goes to infinity of the following:

    The summation (Sigma sum indexed by i bounded from 0 to x) of 9 divided by 10 * 10^i.

    If you compute that, you'll see that the limit goes to 1.

    That's just one unneccessarily complex way to look at it.
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  3. #3
    Member Chokfull's Avatar
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    I like this problem-- 1-\frac {1} {\infty}=.99999999999....

    Therefore, one over infinity equals 0 if \frac {1} {3}*3 is to equal 1.

    This shows that \frac {1} {0} is infinity, also proven by \tan 90^o being \infty, and also being the slope of a vertical line, or \frac {1} {0}
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  4. #4
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    Quote Originally Posted by Chokfull View Post
    I like this problem-- 1-\frac {1} {\infty}=.99999999999....

    Therefore, one over infinity equals 0 if \frac {1} {3}*3 is to equal 1.

    This shows that \frac {1} {0} is infinity, also proven by \tan 90^o being \infty, and also being the slope of a vertical line, or \frac {1} {0}
    \frac{1}{0} is not infinity; it is not defined.

    Usually, we say two numbers x,y \in \mathbb{R} are different, if there exists c \in \mathbb{R}, ~ c \neq 0 such that x-y=c. In this case, what is 1-0.999...? Is it non-zero?
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  5. #5
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    of course you know that 1/{\infty} is nonsense.
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  6. #6
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    Quote Originally Posted by wonderboy1953 View Post
    of course you know that 1/{\infty} is nonsense.
    Not really: was 1/8, but the 8 went to bed...
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  7. #7
    Super Member Bacterius's Avatar
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    Quote Originally Posted by helpwithassgn View Post
    I saw this somewhere but I can't remember the reason behind it.

    1/3 + 1/3 + 1/3 = 1

    1/3 = 0.333333333... recurring

    but then

    0.333333 + 0.333333 + 0.3333333 = 0.999999999...
    The reason for this is that, theoretically, 1/3 + 1/3 + 1/3 is strictly equal to one, but in practice, as no-one can fully represent an infinitely recurring decimal, the sum of 1/3 + 1/3 + 1/3 will tend towards 1 but will never actually reach it. You can't manipulate recurring decimals algebraically without using fractions. Algebra just hasn't been designed for it.

    This is one of the advantages of mathematics in my opinion : by defining some axioms and building everything upon it, it is possible to prove things without actually having to check whether it works : if the axioms remain the same throughout the proof, and the proof is valid, the experimental results will follow.
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