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Proving 0.999... Is Equal To 1
eldavojohn writes "Some of the juiciest parts of mathematics are the really simple statements that cause one to immediately pause and exclaim 'that can't be right!' But a recent 28 page paper in The Montana Mathematics Enthusiast (PDF) spends a great deal of time fielding questions by researchers who have explored this in depth and this seemingly impossibility is further explored in a brief history by Dev Gualtieri who presents the digit manipulation proof: Let a = 0.999... then we can multiply both sides by ten yielding 10a = 9.999... then subtracting a (which is 0.999...) from both sides we get 10a — a = 9.999... — 0.999... which reduces to 9a = 9 and thus a = 1. Mathematicians as far back as Euler have used various means to prove 0.999... = 1."
(0.999...)st Post!
I was able to prove that with even one less "9" after the decimal point, it STILL equaled 1. I plan on doing this for a few more iteration until I can prove that . = 1
See my journal for slashdot ID's by year. Mine created in 2005. http://slashdot.org/journal/289875/slashdot-ids-by-year
Someone disproved math. Kids around the world celebrating. Accountants are lighting themselves on fire. Corporate greed accellerates. 'Office Space' now seen as a prophecy.
Now I can replace my SLA with 100% uptime.
They damn well better, how else will I measure out all this dental floss.
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a+b)(a-b) = b(a-b)
a + b = b
2b = b
2 = 1
Dear Slashdot: next time you want to mess with the site, add a rich-text editor for comments.
In the high school gym, all the girls in the class were lined up against one wall, and all the boys against the opposite wall. Then, every ten seconds, they walked toward each other until they were half the previous distance apart. A mathematician, a physicist, and an engineer were asked, "When will the girls and boys meet?"
The mathematician said: "Never."
The physicist said: "In an infinite amount of time."
The engineer said: "Well... in about two minutes, they'll be close enough for all practical purposes."
0.99999... is equal to 1, then 0.999999...8 is equal to 0.99999... and 0.9999999...7 is equal to 0.999999...6 etc etc etc until 1 = 0! Holy shit!
Or we could just admit that using a tool incorrectly produces idiotic results.
Seven puppies were harmed during the making of this post.
That's a real crowd-pleaser at parties. Personally I like the "writing an executable java program without a main method" trick to impress the ladies myself--that is, if I ever get to meet an actual lady who would even get that trick.
SJW: Someone who has run out of real oppression, and has to fake it.
But you cannot reach infinity so this is a moot point.
I think you just dismissed most of mathematics.
I wasn't trolling :(
Oh... They aren't empty. The aliens live in them now. They think the high radiation is good for their complexion.
No, Ziaxia, I wasn't telling them anything on slashdot, GET OUT OF MY HEAD! GET OUT OF MY HEAD! AHHHHHH!!!! Don't make me explode! ^h^h^h^h^h^hcarrier lost
Self proclaimed typo king, and inventor of the bear destroying coffee table (patent not pending).
Wrong, wrong and wrong.
First off, you're not talking about sets, but separate finite numbers.
Then, infinity is neither rational nor irrational.
Then, all numbers that have "infinite repeating decimals" are rational. See : http://en.wikipedia.org/wiki/Rational_number
So that means 0.999999..... is rational. Which rational you ask? Why! 9/9 :D
Finally, if you say 0.99999999..... is less than 1 : what is the difference between both?
We know it's less than any positive epsilon (0.1, 0.01, or 0.00000.....00001).
Which means it's nil.
There's no place for a single mosquito fart between 0.999999... and 1.
And easy way to explain the Monty Hall problem is.
Lets say there are 100 doors, you pick 1 door. Then someone with knowledge of right/wrong doors opens 98 other wrong doors. There is only 2 doors left the one you picked and probably what is the correct door. Would you switch?
Well, in that specific case, yes :-D.
As a mathematician, I have always hated people who claim that 0.999... = 1 can't be true.
As a nerd, I have always hated people that hate others for trivial reasons. You're just a math bully.
In the high school gym, all the girls in the class were lined up against one wall, and all the boys against the opposite wall. Then, every ten seconds, they walked toward each other until they were half the previous distance apart. A mathematician, a physicist, and an engineer were asked, "When will the girls and boys meet?"
The mathematician said: "Never."
The physicist said: "Eventually, they will come to a point where they would be required to move less than 1.616252(81)×1035 meters closer together. From the uncertainty principle, we know we cannot measure position more accurately than that. So either they will not move at all, or they will superimpose at that point."
The engineer said: "Well... in about two minutes, they'll be close enough for all practical purposes."
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second one orders a half a beer. The third orders a quarter of a beer. The bartender says, "You're all idiots," and pours two beers.
Typical engineer. Here's the operations perspective: .999... means "sometime fail".
a reliability of 1.0 equates to never fail.
a reliability of
The sales guy will sell 1.0, and when failure happens, explain that what was really meant was .999...
Good luck with that.
--
$tar -xvf
I remember being told this in highschool. There was much objection, but the teacher shut us up by simply saying "give me a number in between them."
Duh. 0.9999... and a half!