A question of numbers (one for the maths fans)

Ok then, if you minus one from infinity, you still have infinity?
As a matter of fact, now matter what number you minus from infinity, you'll still have infinity.How can that be?Wouldn't stand true then is you minus infinity from infinity, it can't be done? Doesn't matter how large the number is that your trying to subtract, there will be an infinite number more to replace it. So to me, the equation is unsolvable. Just because there is an infinite number, of numbers to subtract doesn't mean a thing, except that now the equation itself becomes infinite, and never resolves.

Well, there is no last digit. If there were a last digit it wouldn't be infinite. Infinite means you can go on adding digits without ever ending.Like for example the set of integers is infinite. There is no last integer. What ever you take to be the last integer call it n, you can always add 1 to it and then you can add 1 to that. It's infinite and unbounded.An infinite series like .999... is bounded. The bound of that series is 1 and btw did you read any of the web pages I gave you links for? The thing about math is that it is not philosophy. You have to set down and rigorously develop the arguments step by step. It's hard to do in this forum because well, it's one a lot of work, two hard to coordinate, and hard to type math symbols.Just think about there not being any last digit. You know if you multiplied .999... times a thousand you would have 9999.999... and .999... part of that number would be just as infinite as .999...Infinity has that property so to speak. The number of points in a line an inch long is infinite, the same infinite as the number of points in a line a mile long. Infinity equals infinity (well there are infinities that aren't equal but they don't play a role in this).lfen

Hey now, some of us engineers actually get that formal math stuff

That's correct, it's a VERY important mathematical concept.The entire discipline of calculus is largely based upon this concept being valid. The computer you are using is dependent on that concept being valid (electron potential wells, circuit analysis, etc).Infinity is a perfectly valid concept.

To really understand infinity you need to learn about limits and series....Seriously, once you understand inifinite series having finite sums and limits it will all make sense to you.Pre-calculus and introductory calculus is a great place to start.

You've heard of the calculus? That is one of the things it deals with. If you are dealing with unbounded infinities then they just keep getting larger like adding 1 to 1 an infinite number of times.But if you, sticking to this example, add 9/10+9/10^2+9/10^3 and so and on for an infinite number of integer values of the power of 10 and we could write that as .9+.09+.009... or write is as .999... then that sum won't grow huge. If you calculate it for any value you notice that the further you go the closer it gets to one but will never exceed one. so at 10 places it's .9999999999 which is larger than .9 but less than 1. More places gets even closer .999999999999999999999999999.There are proofs which it's been too many years so I don't recall that show that the sum of the infinite series is 1.Take a room that has a finite distance call it 10 feet. There are an infinite number of points in that 10 feet and yet you can walk across the room. You can go .9 of the way, and then .9 of that distance which is .99. Do you wish to claim that you can't walk across the room? clearly the sum of .9+.09 etc in the end is the distance across the room otherwise you would never be able to walk across the room, but you know you do.The above is not a proof but indicates a way to approach a proof.lfen

you subtract infinity from inifinity and get zero.You were asking what ∞ - 1 was. And that's just it. ∞ - 1.Same holds ture for ∞ + 1. It equals inifinity.

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All a man's knowledge comes from his experiences

another source for you on infinity.lfen

But you don't lose a 9, you have exactly the same number of 9s - the only thing that has changed is the position of the decimal point. This happens basically by definition when you multiply by 10 in base 10. More generally when you multiply by n in base n. So we have the same number of digits (infinite), the decimal place has just shifted.Edited by Modulous, : No reason given.Edited by Modulous, : No reason given.

riVeRrat You are asking what happens to the last digit in an infinite series? Have you not heard what has been said? Infinite means no last digit.I am assuming you missed post 102 where I gave a clear explanation {I hope!} so I will ask you to review it and see if it helps clarify.The number is rational and is less of a problem mathematically than a number you are likely familiar with called Pi. You are aware that it is the ratio of a a circle circumference to its daimeter.Are you aware that it is a non-reapeating infinite number? Do you question the reality of it as well?

not quite right.If you subtract to infinities, you can get 0, any number, or infinity.The natural numbers is a infinite set, he natural numbers and zero is an infinite set.subtract the first from the latter and you end up with 1.Of couse it matters how you subtract. Remove all natural numbers from the rational numbers, and you have an infinte set remaining. But order the rational numbers, indexing so you have a first element, second element, etc, and now, for each natural number, N,remove the N'th element from the rational number and you end up with zero elements.In this case the infinity of rational and natural numbers have the same cardinality. You canno do the same with real numbers and natural numbers, since the real numbers are not discrete.The same converns the algebraic numbers and the transcendant numbers, like PI, they are of a different cardinality.

I know you don't lose a 9, but you lost 9/1000. It is clear which one had changed. When dealing with infinity, it is not clear which one has changed, because there is no last digit, that's all I'm saying.
I get it, trust me I do.It's infinite, they all change.But in the equation, there are 2 proof's (?) that show .999 has been multiplied by 10. The decimal moving over, and the last digit going from thousanths to hundreths. When we times an infinite amount of integrers, we only have one proof.Is this because infinity cannot be proven?Also, you have not addressed Message 108Doesn't that prove your formula an incorrect way of showing .999... = 1 ?How can 0.333...= 3 ?Also, can you show that 1=0.999... not .999...=1 ?
In other words, start from 1 and go backwards? and I don't mean just flip the equation.Am I doing something wrong there?

Thanks sidelined. I Get it, really I do. I fully understand the concept you are trying to show me.But that fact that there is no last digit, IS the problem.In a normal subtraction equation, for us, or for a computer, we subtract one column at a time, not all of the simultaneously. Even if we did do it simultaneously, I am finding a problem with subtracting an infinite number from another infinite number, in that the number NEVER ends. So the equation can never end. It can't resolve, just like 10/3 can't resolve.

ifen, for the last time, I understand the CONCEPT of infinity. It's not something I just started thinking about yesterday.You cannot prove infinity. I am 40 years old, and for the first half of my life, I believed infinity could exist. For the second half, I started to doubt it. There is a possibility that infinity does not exist.

From a mathematician's perspective, I have to disagree with that.Subtraction is something you do with numbers. The string of digits written on the paper is not a number. Rather, it is a physical representation of a number.The process you describe with "we subtract one column at a time" is an action on the representations. It is a mechanical procedure we carry out to find the representation of the result of subtraction. That the mechanical procedure is only defined for finite strings of digits, in no way proves that subtraction is impossible. At most, it shows that the mechanical procedure is impossible.Subtraction between numbers can be defined mathematically (or logically if you prefer that term) independent of the details of how we represent the number with ink and paper.