A question of numbers (one for the maths fans)

Wait a sec, can you prove that 10x=9.999... ?just because .999 x 10 = 9.99 doesn't mean that 10x x 0.999... = 9.999...

To multiply by 10, you shift the decimal point one position to the right. Where's the problem?

x=0.333...
10x= 3.333...10x-x= 3.333... - 0.333...3x=3 (*edit here*) the correct answer should be 9x=3x=3
x=0.333...3=0.333...Also, I am still not quite sure how you got 9x=9 out of that equation. I thought it made sense yesterday.Edited by riVeRraT, : added commentEdited by riVeRraT, : fixed wrong answerEdited by riVeRraT, : No reason given.

I can't remember if modulus used the .333 . . . or not.3.333 . . . is not 3. It's 10 / 3QUite naturally, 1 does not equal 1 / 3. (unless they are the zeroes of the equation) Where are you getting x = 1? You have no math in this post to support that.I know from the matter we've been dealing with, x has been 1, but that was dealing with .999 . . ..Now you have a new number, and as such, a new variable.

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All a man's knowledge comes from his experiences

A s mall slip there. 10x-x is 9x, so that last line should be9x=3

small slip indeed.sorry, couldn't stop laughing when I read that. but then, I'm easily amused, so . . .ABE:
of course, I make that kind off mistake a lot too.Edited by kuresu, : No reason given.

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All a man's knowledge comes from his experiences

So in the equation I gave you..999 x 10 = 9.99The decimal place moves over, and you loose a 9 of the end.Well your obvious answer will be that there is an infinite number .999999... and there is no end.But, the last digit has to move over, and it can't since there is no last digit. Does one more digit magically appear the moment we times 10?What is an infinite number minus 1?

So x=3 and x=0.333... ?Doesn't this prove that something is wrong with this equation?

Almost right. If there were a last digit, it would have to move over. But since there is no last digit, there isn't any problem. You still have an infinite string of '9' digits.

infinity +1 ? or - 1?What does it equal? Sure sounds like a problem to me.In the equation 10 x .999 = 9.99 We lost a specific number. 9/1000 .What number do we lose if we are using 0.999... ?

That is elementary algebra. If you multiply both sides of the equation by the same number the equality still holds that is:
w=y and aw=ay
so x=.999... multiply both sides by 10 you have10x=10*.999... to multiply .999... by ten you move the decimal place right and
10x+9.999...This is basic math RR. It's not controversial. It's not debated it done with proofs. Mathematical proofs are probably the most valid deductions you can make. Stop arguing this and instead try and understand it. The {...} is a mathematical convention. It has been proven over and over again that .999... = 1.Now there may be some other way to define this in some special mathematics just like you can assume that parallel lines meet, but in dealing with ordinary world stuff .999... has to equal 1 or we end up with a Zeno's paradox that you can't move. You could never cross a room. Since you can the mathematical concept fits with our everyday experience. You are willing to believe the most unsupported religious things and then you turn around and argue endlessly about well developed mathematics! What gives? You want to live in total subjective fantasy or what?lfen

We don't lose any, because there is always another 9 to the right of it that can replace it.Here is a mathematician's secret. Don't tell anybody.Mathematics is fun precisely because we get to deal with the infinite. If it were not for that, then mathematics would be as boring as accounting balancing your checkbook.Edited by nwr, : reword the last sentence

Just that. In this equation, it's assumed that the nines go on for infinity (that's how it's been treated in this entire thread. So move the decimal place, and you've still got an infinite number of nines following the decimal place.

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All a man's knowledge comes from his experiences

We don't lose any number at all. It's an infinite series and that means it has no last term. If you added 1=1 an infinite number of times you would have an infinitely large number. But the series of .9+.09+.009... approaches a limit and that limit is one.It can never grow larger than one and as you calculate more and more terms the sum gets closer and closer to 1. So the sum of the infinite series can be shown to be 1. That is in the basis of the calculus and it's been too many years for me to recall those proofs.There are infinities but infinity itself is not a number. It may not be intuitive that an infinite series of numbers is bounded but it is a mathematical commonplace.lfen

There is nothing elementary about infinite numbers. This doesn't answer the question of what happens to the last digit. I am not arguing, I have said three times now, I get it. I am questioning it. Isn't that what science and math are all about? Again, I am not arguing, just questioning, the same way I question my faith everyday. Look up the definition of infinity, you'll find out that it is just a concept.