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Wednesday, 20 November 2013

.999... Repeated

Introduction to the Arguments
There are two kinds of people in the world: wedgys and residue folk. They are divided buy their beleif on the value of the repeating decimal .999... (when I write "dot dot dot" it indicates the infinite number, as I am yet to figure out how to make the repeating sign). The arguments are wether .999.. equals 1 or not. This of course is pretty much split halfway, although I personally go with logic and say .999.. does equal 1.

Wedgys believe that .999... does indeed equal 1. It is because with .999.. you cannot get it to one. This means through theorem that if two numbers have no difference or something wedged between them, they must be the same number. Thus .999... is 1. The reasons you ask? Here you go:

  is .333...
We know this because when you divide 10 by 3, 1 by 0.3, 100 by 30, you get .333...
Now the exciting part where I prove this...
Now we know that 3x3 is 9, so .333..x3 is .999...
and that means that because .333... is 1/3, and .333.. x 3 is .999..., and 1/3 times 3 = 1 whole, that .999.. is 3/3 or one whole, so 1.
Impecable logic if you ask me.

Residue believe that with .999... there is still a small amount of numbers, number residue if you will, that is keeping .999... from being 1. Some say that because .999...+.999.. is 1.888... that plus .222.. it will be 2. This is flawed (thank you for spirit of math for teaching me this). .999... plus .999.. is actually 1.999...
The nines never end.. duh duh duh
They feel that there is a small number that can fit between 1 and .999...
Sadly, most mathematicians are wedgys so there is not a lot to back up residue theorem.
But if you have any ideas please comment.

Before you leave comment if you are a wedgy or a residue. Bonus points for providing points to back up residue theorem! Also if you want more math talks please do say so.