The Numbers are Crazy!

Maths is a funny subject. Pretty much everything we use has its roots in maths. Somehow. But strangely enough, the more you think about maths or any specific mathematic theory, the more absurd the whole concept becomes.

Take for instance the question: “Does 0.9 recurring = 1?” Of course not! I hear you cry, because they are both entirely different numbers and no matter how close they are to each other they still can’t be the same. Right…?

Well, consider that the difference between .9 and 1 is .1, and also

from .99 to 1 is .01
from .999 to 1 is .001
from .9999 to 1 is .0001
from .99999 to 1 is .00001

and so on.

Since 0.9r goes on infinitely, we could say that the difference between .99r and 1, for example, is .0r + 1. By logic, this means that the “+1” is infinitely small in all cases and thus 0.9r = 1.

Another way of thinking about it, is that if you multiply 1/3 by 3 on a calculator (remembering that 1/3 = 0.3r), you don’t get 0.9r, you get 1.

Still following me?

Things get confusing though when you begin to consider further, the reasoning behind the above proof.

If we assume for now that 0.9r = 1 thanks to the method shown above, that means after an infinite number of decimal places, the two numbers (0.9r and 1), which would normally be next to each other on a number line, are in fact equal. Based on this, you are basically saying that all consecutive numbers are equal, and thus implying that when you count from 1 to 10, you might as well be saying any random numbers…hmm…

Still not convinced?

Let x=0.9r (Equation 1)
10x=9.9r (Equation 2)
(2)-(1): 9x=9
Therefore x=1

Need more proof?

1/3 + 2/3 = 3/3 => 1/1 => 1

1/3 = 0.3r
2/3 = 0.6r
1/3 + 2/3 = 0.3r + 0.6r
0.3r + 0.6r = 0.9r
0.9r = 1/3 + 2/3 = 1

Crazy Numbers to be continued…

2 Responses

  1. ive disproved these once before, do you really want me to do them again? fine, her goes.

    if you multiply x=0.9r by 10, you get 10x=9.0r (you gained an extra 0.9 that wasnt there before)

    the last one, with 1/3 + 2/3, again its all because of your “convenient” lack of enough decimal places.

    to that degree of accuracy, yes 0.9 is close 1, but if you would like a more exact answer, it wont be.

  2. Thats the latter two false proofs, which I knew were flawed, but the first one (the difference method) is a bit trickier to explain away… ;)

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