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### Mathematical Proof Puzzle

Mathematical Proof Puzzle - 19 November

Below, you will find the mathematical proof that 10 equals 9.99999…. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

1. Τhere is nothing wrong with the proof and as a matter of fact 0,9999...is INDEED 1. (or 9,9999...=10)
If I remember correctly, this kind of proof is attributed to no less than the great mathematician Euler.
Well, the magic of continuum and of the limits...
An other elementary proof /simple thought would be:
Since we can NOT find a number between 9,999... and 10 (and we know that numbers are "dense" ,meaning between 2 different real numbers there is always some other(s)) the two numbers must be the same number. :-)

2. If X=9.999999, then 10X=9.99999, then 10X-X=89.999991 (not 90)..

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4. http://en.wikipedia.org/wiki/0.999...
Note that we are NOT permitted to "stop" the sequence of nines arbitrary at n-th place. The number goes on and on ad infinitum.
99,99999 - 9,9999 =90,00009 but this is not correct
Think simply that equal number of nines at both sides ,works!
99.99999 - 9.9999 =90

5. Gd question

6. No error is present in this proof and 10 is actually equal to 9.99999…. The proof is absolutely correct.