The question came up: does 0.999999999(repeating) = 1?
Several proofs were offered:
1/3 = 0.33333333333(repeating)
multiply both sides of this by 3 to get
3/3 = 0.9999999999999(repeating)
1 = 0.9999999999999(repeating)
x = 0.9999999999999(repeating)
10x = 9.999999999999(repeating)
subtracting the frist equation above from the second gives:
9x = 9
x = 1
But the idea was repulsive to many:
1-0.99999999999999(repeating) = 0????
"There MUST be some infinitesimal difference!!", they said.
The proponents of the proposition agreed, but said, "The proofs don't lie."
My response was
Of course, this limit = 0.
So, DOES 0.9999999999(repeating) = 1?
How could you represent the infinitesimal difference?
I am absolutely opposed to capital punishment!
But I think that I may make an exception for someone posting this question.
This is just a stupid question. Any response is meaningless.
Any person who posts this question is brain dead.
So why reply?
Thanks Skeeter. Thanks Prove It. You two obviously aren't so brain dead that you can't see why someone would ask this question. Plato obviously is. Either that or he's just so much of a jerk that when he feels superior to a questioner he will only respond with insulting dribble making himself feel even more superior. Regardless, I hadn't seen the representations that you two posted. So thanks again.
Hey Plato, thanks for your 2nd and 3rd responses to my question that's not worthy of a response. Your comments are proof that you are indeed the smartest person in the room and now you can sit smugly in your own contented light. Not only have you clearly shown that you know everything better than anyone else, you've also actually provided insight so that I may make a meager attempt to understand a small bit of the knowledge you have long since mastered. You have enlightened my dead brain just a little. Thank you.
And HallsOfIvy - Plato didn't say anything about these being the same number. Instead, he attacked me for asking the question. It was Skeeter and ProveIt who offered additional proofs of the equality. After your post, however, Plato did supply a link to the Wikipedia definition of mondad [sic]. There (in Wikipedia) it clearly shows that the difference between a number and its monad "is infinitesimal". So what I'm walking away with is the fact that this is a topic that even really smart, knowledgeable folks disagree on!
Thanks to everyone!!
P.S. I'm unsubscribing from this thread since I don't feel like reading any more abuse from Plato.
I have to agree, Plato was out of line in this thread.