Actually, there is a number, used in a very specialised area of mathematics, that is infinity. I've already mentioned it - Aleph-1. Then, of course, there's Aleph-2 and so forth, all of them infinities, but if n>m then Aleph-n>Aleph-m.

Aleph-1 is the number of integers that exist. Aleph-2 is the number of real numbers that exist.

So what you're saying, SOlbadguy500, is that 1 / (10 ^ (infinity + 1)) is, in fact, NOT 0?

yes. 0.9R approaches 1, not infinity. But the 9's are infinite. So it's the idea of taking an infinite number of 9's minus an infinite number of 9's. Regardless that the decimal there, it is an infinite number of 9's, and that is what you can't subtract.

which is why i've mentioned other values with an infinite number of digits that *can* be subtracted from other values. you can do 1/3 - 1/3, which is 0.3R - 0.3R. you can't say that 0.9R cannot be subtracted only because it has an infinite number of decimal places, you'd have to explain why 0.9R is somehow different than other repeating decimals.

like i've said before, this has nothing to do with different degrees of infinity. both 0.9R and 9.9R have a number of decimal places equal to the set of integers. you can claim that 0.9R has one more nine, but one more nine is hardly the difference than the number of real numbers and integers.

f(x) = x
g(x) = x - 1

as x goes to infinity, both f(x) and g(x) go to the same infinity, even though f(x) is one "ahead" of g(x).

Hehe, how long has this argument been going on? It seems like it's been a week.

how would any number not result in zero when subtracted from itself?

1 / 3 - 1 / 3 = (1 - 1) / 3

(1 - 1) / 3 = 0 / 3

0 / 3 = 0

that comes out to zero. not a number close to zero, but *actually* zero. if it comes out to anything different than zero, show why all of this math is incorrect and show me the value that it really comes out to (and don't try that 0.0R1 nonsense, we've already been over that :-P).

But if you're saying that .9R is a constant, then you have to admit that you can divide a constant by 10 and get a different number.

i'm not sure what you mean there.

0.9R / 10 would be 0.09R. those are different numbers, they differ by 0.9.

that algebra is what got this whole thing started, lummox ;-)

people had problems with doing 9.9R - 0.9R. solbadguy said it can't be done because of the infinite number of nines. all the decimal places are nines, how would you know that they all cancel out? ;-)

also, jp said that 9.9R would have one less nine after the decimal point than 0.9R, which he went on to explain in great depth and made a whole lot of sense (not really).

i think the biggest thing that throws people off about this is that you've never had to deal with 0.9R before, because a calculation wouldn't result in 0.9R, it would result in 1. so, you'd never really think about it because there was never a need to say "0.9R".

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Which I guess is all just a long way of saying that people who are bad at math shouldn't talk about it.
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Now that is hurtful, Lummox.

One series is a nine ahead of the other. But that 'nine ahead' gets smaller and smaller as you let the digits go to infinity, and that's the argument that convinced me (a while ago) that 0.9R=1.

And that, of course, discredits my counterproof about this, because my counterproof revolves around a number I've designated '0.0R1', or an infinite number of zeroes with a one at the end, and that's as much a zero as 0.0R9, which is the 'nine ahead' of 0.9R when it goes to infinity.

Lummox, shut up you don't know anything about this.

he might not know too much about this particular "debate" we've been having, but he does know a thing or two about math.

Algebra doesn't prove what you're saying.

well its not a proof in the strictest sense, but it does show that 0.9R equals 1.

You're letting the laws of ininity be what you want them to be.

i don't think you know what the laws really are, so you wouldn't know if he was using them incorrectly. an accusation like that isn't very convincing when you don't explain his mistake or correct him.

You say that .9R is a constant that can be subtracted from itself. If that's the case, then 9.9R/ 10 = 0.9R but the 0.9R would be smaller by one 9 then the 9.9R. See, it doesn't work. So it can't be a constant.

i'm not sure what you mean there, but 0.9R is as constant as numbers get. whatever its value is, that value never changes. whether you think its 1 or not, the value of 0.9R is always the same. despite having an infinite number of decimal places, its value is finite. 1/3, pi, and the square root of two are all constants, and they all have an infinite number of decimal places.

It just keeps going 9/10 + 9/100 + 9/1000, and on and on and on. Tell me what point in that geometric series it would equal 1 please.

when you have infinite terms.

I don't understand how going in that direction would actually equal 1.

we've mentioned and given links to a lot of proofs and explanations. i'm not sure why you don't understand this because you don't really explain why you believe what you do. so, its hard to see what exactly you're missing here.

Now, if you want to say that it infinitely approaches 1, then you would be right.

the series has terms and as you add more terms its sum approaches a value. 0.9R is the summation of that series with infinite terms. since its a constant, the value of 0.9R does not approach something, its value *is* something. it already has an infinite number of digits, so its value isn't approaching 1, it is 1.

I honestly don't think that a infinity number exists.(did I mention I'm more into theory than anything?) even with the argument of any of these calculations they really have no basis, because its still equals a number, as does any other calculation.
it may go on into the number as 0.9999999999... ad naseum. but in the end its still a number.
and still a equation. therefore not infinate.
To create infinity you have to make a impossible math problem, one that cannot be solved through any means. only then can infinity be discovered

"i honestly don't think that you read lummox's comment where he said "people who are bad at math shouldn't talk about it." you can tack on "because I don't understand math." to the end of any of your sentences and it works."

I honestly don't think you use your head or you would figure out that his comment got me to actually post a reply. Because you don't agree with me doesn't mean that I don't understand math. Don't think you have every mathmetician out there agreeing with you, but you wouldn't think that, no that's ignorant. .9R never reaches 1, now you can go ahead and use algebra, series, limits, whatever the hell you want, but I'm done arguing this. You just find different ways to express the same thing and then say I suck at math for not having addressed it. Of course it's easy to say .9R equals 1. But it isn't logical. Instead of replying to this in 5 minutes like you usually do, why don't you think about it. Think about my real world example, except without time constraints. 10 feet from a wall. Keep getting a fraction closer to it. Do this for infinity and technically you should never hit it. Stop trying to say you would hit it.