0.99999~ = 1 ?

Surely the difference between 0.999R and 1 is practically non-existant and philosophically massive?It is the difference between claiming complete certainty (for example) and always allowing for the possibility of that which is unexpected (no matter how likely or unlikely). It is the difference between an obtainable destination and that which can never exist or be obtained in reality.I am no mathematician. But surely the difference between 1 and NOT 1 is as significant as ever. No matter what the NOT 1 may be?Edited by Straggler, : No reason given.

Well It appears that the genaral consensus amongst those who are more mathematically literate than myself is that I am wrong.In which case I stand corrected. And in which case I will need to find a new nomenclature for expressing all but certain without the philosophical possibility of complete and absolute certainty.But just to be clear is it false to say that 0.999R < 1?

This is a genuine question. As it appears that my understanding up until now has been incomplete (to put it politely - or just wrong if we are to be more blunt.But is it wrong to say that 0.999R <1?

Well up until now I have (rightly or wrongly) been expressing the difference between probablistic certainty or otherwise as the differnce between 1 and NOT 1. Where (in my mind at least) 0.999R is not equal to 1.It appears I am need to change my nomenclature. But I am not sure what I should use instead? Well I get what you are saying. I think. But it still seems counter-intuitive that 1/0.999R is entirely equal to 1/1. For example.

Double post. See below.Edited by Straggler, : No reason given.

Yeah I am starting to get that despite inbuilt resistance. Can it be shown mathematically that 1 - 0.999R is equal to zero? One step further down the infinite chain than you need to go to make 0.999R the same as 1?

Fair enough. Is there somewhere I can see the mathematical proof of that? Well is infinity + 1 > infinity. I guess not. But even in my fairly limited context of undergraduate level physics (as opposed to pure or higher level maths) the concept of more rapidly approaching infinity and thus "degrees of infinity" has arisen. At least in some sort of conceptual principle.So even if I am taking the role of the idiotic punchbag for the more mathematically literate here I do so on the basis of asking whether things are as obvious as you seem to be claiming?

Put like that - I guess so.But does that mean that infinity squared is the same as infinity to the power of 10? For example. Well I had to try. Yes. But once we start invoking infinity all sorts of mad sounding stuff is mathematically true in ways that mathematicians I have spoken to never sound wholly convinced by themselves in ways that are well beyond me to know why they have such arguments.Maybe I am extrapoloting too far. Maybe every mathematician would say that 1=0.999R exactly and without any reservation of any sort. Without any debatable notion of infinity being involved.I am just not knowledgeable enough to say. But it still strikes me that once you need to invoke infinity nothing is as cut and dried as seems to be being asserted here.Edited by Straggler, : No reason given.

Screwed if I know. But then degrees of infinity is no less mad and that is a genuine mathematical concept. Well once we invoke infinity we can make all sorts of stuff sound insane. Wich is kinda the problem with invoking infinities. They are not very practically helpful. So I am told. In my limited experience maths guys can argue about the nature and application of infinity infinitely.

Well I accept what you say. And when you guys explain it does all kinda make sense. But there is still something that seems intuitively wrong about the whole thing. For example is it true to say that 0.999R is a whole number? Thanks for this. That does actually make sense. Even to me.

I get all the arguments for 0.999R being entirely equalt to 1. But it still seems "wrong" that 0.999R is a whole number. Surely I am not alone in this intuitive feeling? Otherwise it wouldn't even be a topic worth highlighting. Oh God. Please. Let's not go there. You know what I mean about the inherent impossibility of certainty in evidence based arguments just as well as I do.

I don't think so. I think it is because the human brian (well mine at least) cannot cope with infinity. And for this to make sense we need to think of 0.99999999999 - to infinity.If I were to say that the difference between 1 and 0.999R was 0.00R1 I would be talking mathematical nonsense. I don't dispute that at all.But I still think pretty much everyone here would have a vaguely instinctive understanding of the cencept I am trying to convey.So I think it is more than just presentation. I think it is our inabilioty to really conceptualise infinity that lies at the heart of my self proclaimed unease.

I think the lack of intuitivity comes about because we need to think in terms of infinity.The concept of infinity doesn't come naturally. What's more if we are going to accept infinity as a reasonable concept then it also intuitively seems no more or less reasonable to accept the concept of infinitesimal. In which case saying that:1 > 0.999... by an infinitesimal amount sounds more intuitively reasonable than saying 1=0.999R Yep I accept that. I am simply arguing out of bloody minded obstinacy at this point. Not because I think I have a mathematical case for refuting anything being said here.But it is interesrting looking at ones own thought processes and trying to work out why something that is so logically provable seems intuitively so wrong.

Well sure.Except that it still seems like 0.999R should be infinitesimally less than 1. Which I suppose it is. If by infinitesimally small we mean tending to 0.Which brings us to distinguishing between 0 and something that is infinitesimally small. Which brings us to distinguishing between something and nothing. Which is where I think the whole intuition things takes over and gets things wrong.

Well it's nice not to be the only lunatic in the asylum Yeah I figured that one out for myself. But it still feels wrong don't it?