Seltzer

Look, I know it seems counter-intuitive to believe that 0.9 recurring = 1, but you have to trust me on this one Your reasoning follows on from this:

2 - 1.9 = 0.1 = 10^-1 (which is more than 0)
2 - 1.99 = 0.01 = 10^-2 (ditto)
2 - 1.999 = 0.001 = 10^-3 (ditto)

General Form:
2 - 1.9{n} = 10^-n where 9 is repeated n times (which is more than 0)

That reasoning is fine for a finite n. But as n tends towards infinity, limit(10^-n) = 0. In other words, that 0.000...001 number you quoted is basically 1/∞ which is considered to be zero, meaning that 2 - 1.999... = 0 (which makes sense since 2 is 1.999...)


Here's another simple proof that 0.9... = 1. This is a method commonly used to convert recurring decimals into fractions and it demonstrates that 0.9... is 1/1 as a fraction.

x = 0.999...
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 9/9 = 1, therefore 0.999... = 1


The important thing to understand is that 1.000... and 0.999... are both decimal representations of them same number (1). This applies to other numbers too (i.e. 0.8324 = 0.8323999... ) but not to all numbers (i.e. 1/3 = 0.3... and there is no other decimal representation).

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TheBig3

Did we really bring the nerd-dom of MMO's to MB?

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Seltzer

MMOers wish they could be this nerdy

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TheBig3

Oh really? Then feast your virgin eyes upon the godless math skills of the Theorycrafters at Elitist Jerks...Behold!

http://elitistjerks.com/f47/t82625-shaman_elemental/

Don't even read the page, just scroll down and watch the formulas and graphs scroll by. This is for one spec, of one class, in one video game - nerds.

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Seltzer

WoW nerds do put an impressive amount of effort into theorycrafting. I also came across this recently - it's an academic paper written about the probabilities of getting various skills when leveling up in Heroes III

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noise

it's good news that .9 repeated is the same as 1, otherwise i'd never make it home (i'd just get closer, and closer, and closer... but never quite there!)

of course, if you break my journey down into an infinite number of steps, each step is zero meters... so how will i ever get home?

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swim

You can find the sum of geometric series that converge. Thus you can find the sum or rational form of a repeating decimal. By using n/(1-r)

.9/(1-.1)=.9/.9=1

I'm a math major
this is fact
close thread

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TheBig3

I'm kinda turned on right now.

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Dr.Seussicide

Yes, 0.9999 recurring can be mathematically defined as 1. In fact, in many applications, including aerospace engineering, the specificity of a number is usually used to the 5th decimal place. Anymore than this would usually be supercilious. For example when using pi, 3.14159 is the generally accepted figure to be used.

Here's a fun fact for math nerds, the closest fraction for pi was found to be 355/113. Not 22/7 which was probably used when you were about 9years old to calculate circumference.

So at any rate, 0.9999 can be substituted as 1 in any mathematical circumstance. It can be proved as a proof as Seltzer did or simply by common sense as I have just shown here.

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noise

is this like a cross between "super silly" and "super serious"?

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