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Here's The ORIGINAL Equation That Proved 0.9(repeated)=1 :)

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Posted by Larry J. Rhodes on October 18, 2002 11:59:46 UTC

It was actually my high school algebra teacher, Mr. Townsend, who first "discovered" this equation. Do your'll find he was was credited for this little conundrum.

Okay...let's assign 0.9- (can't put it OVER the nine, so I'll put it beside it) a variable...


Let's multiply both sides by ten.


Now, let's subtract our oringinal equation from our new one, which we all know is a perfectly acceptable mathematical thing to do.


What do you get?


Divide both sides by 9, and you get


Well, if x=1 after all of these perfectly valid steps, yet it started out equalling 0.9-, then it MUST be true that 0.9- = 1, right? Nope.

There are some things outside the limits of math as we know it. But they are as rare any any of the other phenomena that are outside our understanding, such as antimatter and the like. I often use this to demonstrate the fact that, no matter how complicated you try to make things, very little will ever make up for good old fashioned common sense. We KNOW, rationally, that these two numbers do not equal each other, and all the mathematical equations in the known universe can make it FACT. ;)

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