if two numbers can be so close that no number is in between them, what comes before 0.9R?

uh oh, you phrased the same thing in a slightly different way. That must mean you are right and i'm wrong. Look man, you can't subtract infinity from infinity and get 0. It isn't a constant. It's an abstract idea.

i have no idea what you're talking about there. i was not subtracting infinity, i was subtracting an infinite series. 0.9R is not infinity, it just has an infinite number of decimal places. if the amount of decimal places bothers you, since its a repeating decimal you should just write it as a fraction instead.

there isn't an extra nine, all terms in the series can be mapped to the set of integers.

Alright fine. Let me rephrase then. you can't subtract infinity, even if is an infinite number of decimal places. The whole infinity thing I was talking about was 9.9999R - .9999R = 9. You can't do that. That was subtracting infinity. You get it now?

no, i don't "get it". could you explain why it cannot be done.

and you never addressed this: if two numbers can be so close that no number is in between them, what comes before 0.9R?

"nd you never addressed this: if two numbers can be so close that no number is in between them, what comes before 0.9R?"

ummm, .9R with an 8 at the end ;)

You're right. I think the modified version would be something like .999R + 8/inf. I wonder if that number exists, but it's the closest I can think of. Eventually on the numberline, as you go to infinity, numbers won't have anything in between them. There's thousands of examples. It isn't just I.9R, 2.9R, etc. It could be 1.19R being next to 1.2, 1.1119R being next to 1.112, 1.3459R being next to 1.346. Those are the ones that are easiest to be defined. Now i'm sure that the ones that are harder to define ( ex. what is before .9R ) do actually exist. By the way Fish, i'm getting a little bored with you just asking questions. Jp asked you a question. Why don't you answer that or something. Just in conclusion, i'll summarize one of my old main arguments. .999R isn't 1, it just infinitely gets closer. Hypothetically, it's like standing 10 feet from a wall and always walking a fraction of the distance. Now, in theory, you should never reach the wall. Of course you couldn't try this in real life because it is impractical, however theoretically it works. It's the same concept.

"i ask questions because you don't explain your reasoning for thinking what you think. if you do have some reasoning, then you should be able to answer the questions no problem"

It's not that, it just feels like i'm talking and getting no where. I mean, i've convinced a few people, but you seem like the type that'll keep this going forever unless it's closed.

"the limit of 8/x as x goes to infinity is zero. you can't plug infinity in for x, but you can find the value that 8/x approaches."

Same concept. 8/inf approaches 0. It's just so damn small but still not zero

"as i've explained to you before, it doesn't work because of the time constraints. taking a step takes a certain amount of time, and people only live so long. it takes no time for 0.9R to have decimal places, so its not the same concept. your example has a problem that this mathematical idea does not have. also, 0.9R is not equivalent to just walking any old "fraction of the distance". if each step moved you 1/10th of the way closer to the wall, you would never hit it, like how 0.1R != 1."

I thought you'd get it if I reworded it. Notice I said hypothetically, meaning in theory. It's a physical comparison, but I didn't mean you actually try it. It's just something to compare it to. And yes, any fraction between 0 and 1 would work. It's the idea of it going to infinity but never hitting the wall. You'd be saying that it would hit the wall. Now, i'll say it again, maybe you'll get it this time..... IN THEORY, NOT IN PRACTICE.

"you'll never understand things like this if you always want a physical example."

you'll never understand things like this if you are dismiss the example because of your silly time constraints.

Alright, all explain why you can't subtract infinity. Because it is not a constant. It represents something that never ends. So how do you know that you can just subtract it? What would it be since it's not a constant? 1? 2? 3? You can't know for sure. And you say they have to all cancel out? How do you know they cancel out to 0? Why don't you explailn that? And i'll say it again, dont just say it's a constant, because it isn't. Or because it's looks the same after the decimal point.

" understand what you're saying, but those constraints are what makes your example not work. because those constraints only apply to your hypothetical situation and not to the actual math, its not a very good example."

I suppose it's not a good example because someone like you would add an unneeded factor ( time ) to the problem so that you can dismiss it as a bad problem, and then ask questions about it. Assuming time was infinite, answer the question, you would never get to the wall, would you? Same thing here. You never get to 1.

"any fraction? what's 0.9R as a fraction? ;-)"

Any number between 0 and 1 then. And any number can be made into a fraction, besides 0 and infinity of course. 9.9R / 10 maybe? <_< Goddamn, stop with the annoying specifics. You already should know that I mean number. And if it isn't directly said, then use your math skill to figure out that any number can be made a fraction.

Well something like .875 is rational because it is 7/8. But something like .8430873209475745934..... isn't because you can't determine the fraction other than something like 8.43087.../10. He was being vague, so I played into it. I know what rationality is.

"0.9R is a constant, and you can subtract it from 0.9R"

I guess that's the main reason we see this differently. I view 0.9R as going to infinity, and since you don't, let's just agree to disagree.

I was trying to get you to drop it. But since you responded, so will I. .9R goes to infinity since it has infinite 9's. Is that concept so hard to get?

" the value of 0.9R is somewhere between 0 and 1 "

It seems this argument is done though. You agree with me. 0.9R is between 0 and 1.

"i don't like to think of what i do as disagreeing, but being correct."

You're correct now since you finally agreed with me. 0.9R is it's own separate number. You even admitted it up there. The winner is me. You go to hell. Burn

"there's a difference between having an infinite number of decimal places and "going to infinity". "

The 9's go to infinity. Seriously, I thought that would be easy to figure out. Either i'm not arguing with the sharpest tool in the shed, or you're just trying to avoid it.

"like i've mentioned before (and you've never addressed it), why can you not do math with a number that has an infinite number of digits? you never explained that, you just said (repeatedly) that it cannot be done. however, its done all the time. one third, pi, and the square root of two all have an infinite number of digits, but they occur in math rather often. how can you subtract 0.3R from something but not be able to subtract 0.9R from something?"

I wouldn't agree that pi minus pi would necessarily be 0, assuming the digits are infinite. I don't know whether pi is infinite or not. It probably is. But in math, the differences are so negligible that you just assume that 3.33333R - .33333R = 3. even though, if you were to keep subtracting like that, you'd get .0000R1. But in a problem, that kind of little thing doesn't matter. When discussing the absolute value here, it does. How else do you want me to explain why you can't subtract infinity. I thought I already have, but i'll make it more formal. Infinity isn't a constant, it's a concept. When I was doing limits in calculus, it was tempting to subtract infinities. But our teacher says that calculus doesn't allow for it. Since infinity isn't a defined number, you wouldn't know what the answer would be when you subtract them, so it is futile. That's what I learned, and it makes sense.

"i said "inclusive", meaning that the value could be anything between zero and one, *including* zero and one."

All right, i'll give you credit for that, I didn't see that.

"calling this an argument is giving you much more credit than you deserve. "nuh uh" is not much of an argument."

That's pretty low, calling my argument a "nuh uh" and saying I don't deserve this. Who defined you as being right? Don't act so judgemental without thinking about your own agrument first.