Hi James.

Sorry for the tardy reply, but Trippy banned me for 14 days after I pointed out his transgressions against site rules and other members. I will be sending you a PM as soon as I get time to compile it (unless Trippy bans me permanently first to prevent it!). Anyhow, I am very busy, as you may be aware by now, so I must be brief in this present reply to yours above. If by any chance Trippy permabans me before I PM you, I'd just like to say it was nice knowing you; and that I have the impression you have been doing your level best with the most blunt and oh-too-human 'modding' tools/staff available to you under the circumstances.

Anyhow, to your post...

Undefined:

You've posted a huge long post, yet *still* failed to answer the question I asked you. I remind you:

1/2 + 1/4 + 1/8 + ... = 1. True or false?

This is a mathematical statement. Either you think it is true, or you think it's false. There's no half-way house. So, which is it?

Let's look at some of what you wrote. I really don't want to wade through all of it.

I have not demanded anything of you. Here you are, making post after post in this thread, yet you seemingly don't have an actual point of view on the simple question above. All I see is waffle.

Also, didn't anybody ever tell you that using ALL CAPITALS on the internet is considered to be SHOUTING? Do you want to look like some kind of deranged nut? Because that's the kind of person who mostly uses random capitals on the internet.

I'm having trouble unpacking what you even mean by all that. All those CAPITALS for emphasis, and you still haven't communicated.

Very often indeed, I'm sure. What's wrong with that?

Not by me. Not at this stage.

I wouldn't have thought that answering a simple question like the one above, about your own personal beliefs, would be as hard as it apparently is for you. Maybe you should just leave this thread alone.

Does this mean that you're leaning towards saying the statement above is false, then? I really can't tell.

Forget my arguments. How do you respond to post #915, above? That has put the nail in the coffin in this thread, as far as I'm concerned. What's your analysis of that?

Nobody has asked you about reality and unreality. For my part, I simply want to know whether you agree with the truth of the above mathematical statement. It's a formal mathematical statement in a formal mathematical system. So, within that system, is it true or false?

And, while we're at it, is it true that, in the same system, 0.999... = 1?

One you've answered those questions, *then* maybe we can start getting all philosophical and start pondering whether this formal mathematics actually works in "real" world, whatever that is.

Ok. So help me.

Explain to me what is patently incomplete about my orthodoxy. Because it isn't patent to me at the present time.

Do you include post #915 in that?

You seem to think that a number is a process. Or do I have you wrong?

Also, I'm puzzled as to what you think is "real" about a number such as 7 or 1 or pi. I'd say all numbers are abstractions. We can talk about the number 3, but it's an abstraction until we start talking about 3 sheep or 3 dollars or 3 tons of salt.

It now sounds like you're saying you have no idea whether 0.999... = 1 or not. Is that correct?

I think you've misunderstood Goedel. Of course you can use arguments within a formal system to prove statements made within that system. If you couldn't all mathematics would be useless. Goedel's theorems are about the completeness and consistency of formal systems.

So, tell me how REALITY would work out whether 0.999... = 1 or not.

I don't think Motor Daddy has pointed out anything of the kind to me.

Maybe you can explain without all the CAPITALS and waffle.

I thought it nicely demonstrated the point that 1 thing can be divided equally into 3 parts, which was an issue Motor Daddy disputed at the time. Now, he appears to be running away from that silly claim. But perhaps you'd like to take up his baton?

Nobody's talking "real" yet. This thread is about the mathematical truth or falsity of 0.999... = 1, isn't it?

This sounds (a) like you think that 1/2 + 1/4 + 1/8 + ... doesn't equal 1, and (b) like you think a number is a process.

Do you want to address either of these points in more depth?

May I remind you and everyone that, as the "Philosophy of Maths' in the title implies, and as the location of this thread under the "Philosophy" section further stresses, this thread was opened for the express purpose of delving behind the maths system itself as it is currently constructed and practiced. That is why my responses to you here have been directed and based on the Philosophy and starting axioms etc origins' and 'adequacy' etc. So please do not think I am trying to evade your questions just because I am replying in the context of the philosophy/axioms and practice which led to the current expressions/arguments you and others keep 'challenging' me to answer in the current maths context rather than in the maths Philosophy-and-Axioms-questioning context which is what this thread is all about.

If you have read my replies to arfa et al in the context of philosophy/axioms, you should have noticed that I pointed out that 'point' is a philosophical notion only, and not a 'self-evident' fact. Hence the potential for GIGO from that starting 'point' axiom, irrespective of how 'rigorous' may be the following 'logics' based on such NON-rigorous and NON-maths starting axiom/point; which is why I pointed out the undefined, undetermined and singular/infinite are inescapable in such an 'iffy' maths/logic flowing from such an 'iffy' starting point/axiom. I already posted to Trippy where the like/like construction is fraught with peril from the get-go, else 0/0 would be as valid and meaningful as 9/9 IF "0" is a number on the extended or 'ring' number line. I have also given my observations on '0' in many contextual settings, including the obvious physical reality context, so I will not repeat them here either. Moreover, the way 'infinity' is being bandied about in the current (supposedly rigorously logical maths treatments) is obviously flawed also from the get-go, so GIGO is also inevitable, as all the 'infinities' which arise at present well demonstrate (by the way, I have also mentioned before that I have identified blatant logical flaws in all the currently accepted Hilbert's Hotel type treatments/assumptions of infinities. I have effectively demoloshed Hilbert's Hotel and all its like infinity 'arguments/treatments'; and the details will be published in my ToE book).

So, in that context and in keeping with the thrust of this tread, I will now briefly reply to some of your and others 'assumptions' and 'challenges' as the current maths poses/accepts them as so-called' proofs (as the current maths 'produces' but which do not answer as 'proofs' when the whole starting/background axiomatic philosophy aspects are brought into it to examine the validity or otherwise in the wider context, including the reality context of physics which maths purports to 'model'). I begin with your above reiterated question:

James R said:

1/2 + 1/4 + 1/8 + ... = 1. True or false?

I was loathe to answer this before because the expression as constructed (according to current maths axioms/assumptions) does not have regard to the 'infinitesimal of last effectiveness step' which the logical extension of "..." will eventually run up against under any reasonable reality/logical context that is not flawed by the inadequacies of the current maths axiomatic start from the purely philosophical notion of 'point' which allows an infinite-points extension without any end (that is a purely philosophical assumption BUILT INTO that and 0.999... etc type expressions. The problem is that, as I pointed out before, there must be an ultimate step quantum for any series whether in reality or in logic, else it is a purely philosophical expression and not any sort of rigorously mathematical expression. Hence the GIGO potential which I have been addressing by pointing out (as this thread requires) where the starting axioms/assumptions and following arguments may be at fault and lead to such mathematical non-sequiturs which when examined are found to be purely philosophical expressions, without any real maths meaning or capability of treating them to arrive at any rigorously valid conclusions/claims about what that "..." means in any context, let alone in a maths context which is ultimately found to be based on purely philosophical starting premises which have no regard for either the logic or the reality of an ultimate step quantum of effectiveness in all contexts, be they maths constructs or physics realities.

Hence my answer, in the specific philosophy-of-maths context and thrust of this thread, can only be:

It depends on whether your 'expression' can 'handle' that ultimate smallest quantum step to transition from one 'state/frame' to the next state/frame via a 'transitional singularity state of SUPER-positioning' factors/values which cannot be properly 'divorced from' logics and physics by purely ad hoc and invalid philosophical/arbitrary 'fixes' as one goes along an already flawed-from-the-get-go' mathematical system that still outputs undefined, undeterminable and infinities etc.

**Now IF we include the inescapable (logically and physically) ultimate step quantum of minimal effectiveness (INFINITESIMAL) into the axiomatic system/treatments, then such an expression as you posted above will be read as "..." indicating there will BE some transitional infinitesimal (currently not included in the maths axioms/construct as it stands at present) which EFFECTIVELY TERMINATES the series and transitions that series into an END STATE of "1" which is also the BEGINNING STATE for whatever comes next from there.**
See where I am answering within the purview and thrust of this 'philosophy of maths' thread? Please then do not accuse me of avoiding, just because you are talking about the maths as is while I am talking about the philosophy/axioms from which the maths-as-is has been apparently ad-hocly and non-rigorously 'developed' to the point of it becoming meaninglessly infested with undetermined, undefined and infinities and obvious ill-logics and miss-assumptions being built into it, as I have already observed with supporting logical/reality (not philosophical like the mathematicians have been basically doing with their 'proofs' and expressions etc) based arguments more than once now here and elsewhere.

And speaking of infinities and the absurdities which start the maths of such, I draw your attention to this from rpenner to hansda:

It doesn't matter what I believe. It matters which mathematical axioms I choose to work with. Different axioms, different results. In this case $$\infty$$ as a quasi-number is only defined in one of the two systems I talk about and in that system $$T_{\infty+1} = \frac{1}{10} T_{\infty} = 0$$.

But neither of those two systems is necessary to everything in [post=3164396]Post #915[/post] being correct.

Now I ask you, James R, everyone, how can maths system 'choose' to start/base their following logics and treatments and results from such an obviously absurd 'axiom'?

**Consider: Once an "$$\infty$$" has been invoked into an expression, how can anyone logically, physically (or even philosophically for that matter!) possibly pretend that they can "add 1" to such a thing?**
The invocation of an infinity effectively creates a boundary condition beyond which there is only a DIFFERENT STATE and so no longer within that 'starting' infinity as invoked.

**In short: If we add 'anything more' to one infinity as invoked, it becomes ANOTHER infinity altogether. The former bounds its starting context; and any variation to it is impossible in any sense, and only can CHANGE the NATURE of that starting infinity to some other 'infinity' conceptualization.**
See where the maths as currently formulated and 'practiced' wants it 'all ways' but cannot deliver in a 'consistent way, hence all the slippery a hoc assumptions/philosophical 'fixes' necessary to 'make it work at all'? The undefined, undetermined, and slippery logics/non-sequiturs (as perfectly exampled by that above axiomatic 'choice/treatment' in order to 'allow' that above absurdly dreamed up $$\infty+1$$ nonsense) should obviously be, especially in the absence of any real 'current maths' understanding of what infinities and infinitesimals really are, a cause of serious concern to all thinking people who can go beyond the circuitous and axiomatically inadequate self-selecting illogics/constructs currently being claimed as 'rigorous maths system'. The problem with that claim to 'rigour' etc, as I have shown already, is that it starts out all wrong, and has become a SELF-PERPETUATING GIGO system which needs on-the-fly 'fixes and non-sequiturs' to 'paper over the cracks which extend from the starting 'point' philosophy that makes nonsense of all the rest and prevented mathematicians from actually starting from axioms which are reality/logically founded and which would if followed properly provide understanding/treatments of infinities, infinitesimals and 'zero' and etc which void all the current undetermined/undefined etc nonsense outputs which perfectly demonstrate the inadequacy of the current maths/axioms/assumptions/treatments etc.

**That above, and my previous here and elsewhere, is basically all I have to say on these matters until I publish the whole lot complete. Good luck and enjoy your further discussions/explorations, James, everyone!**
James, I have been as brief as I could while still providing you with the essential thrust of my points/observations in the context of this thread regarding the philosophy etc of the maths and how I have been working to improve it so it can be started again from real/logical axioms instead of purely slippery/philosophical 'notions' it has been riddled with from the get go. As I 'pointed' out many times already. I have run out of time for now. So I will get back to you via PM about that 'other matter' (if I am not permabanned by 'you know who' before I get a chance to put my version/evidence to you!). Either way. No hard feelings, mate. I mean that sincerely, as always (regardless of whether certain troll-mods still have a hard time believing such a thing is possible given their individual/collective transgressions history).

Cheers James. Take care not to let your deference to certain 'types' lead your intellect and integrity into being too easily 'swayed' and 'captured' by the 'maths-without-sense' crowd and/or 'mod-troll gang leftovers' from the bad old days. Without true examination of 'orthodoxy' as currently assumed/practiced, no further real advance to towards the complete maths/physics ToE will be possible. Hence my taking risks such as these to point out the obvious flaws at present. I am entirely independent researcher/thinker upon the universal phenomena, and beholden to no 'group think' or 'publish or perish' imperative' or 'peer pressure grouping' etc crowd. I trust that will have been made abundantly clear by now to you and all thinking observers/forummers? Bye for now!