Why 0.9999… Equals 1
February 4th, 2017 by Math Tricks  Filed under Math Tricks.
Here is an illustration as to why 0.9999 (dot, dot, dot . . . ) is equal to one:
Do you see a problem with this “proof”?
Tags: Rounding Up
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Here is an illustration as to why 0.9999 (dot, dot, dot . . . ) is equal to one:
Do you see a problem with this “proof”?
Tags: Rounding Up
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There’s no issue with this proof. It’s simply a matter of accepting the mathematical laws of equality and inequality.
If not, the discussion is over.
I find most have issue with this because of confusion between infinity and an infinite number of things.
Not all infinity’s are the same. 0.999… has an infinite number of 9’s after the decimal whereas 10 X 0.999… has an infinite – 1 number of 9’s after the decimal. both are infinities, but are different. If you could ever reach infinity (which you can’t) then when you do the following step:
10x – x = 9.999… – 0.999…
simplifying it would look like this
9x8.999…991
which would again make x = 0.9999…
sorry, typo, should be: 9x=8.999…991 and not 9x8.999…991