James R said:

I've asked you twice now, and you haven't managed to answer the question yet.

1/2 + 1/4 + 1/8 + ... = 1

True or false?

A bit strange, isn’t, that you demand an answer from someone whom you just ‘sent off the field’’ for three days, so preventing him from responding?

And you wanting it both ways by demanding an answer from me that you ‘want’ over what my answer MUST LOGICALLY BE consistent with all the context/discussion/explanations so far in this thread that points to YOUR stance being UNreal and hence UNANSWERABLE in any way that is real and meaningful when the very BASIS of your stance is the whole POINT of this thread/discussion, seems a little disingenuous. Not to mention the patent double-standards you are using to excuse your ‘emotional response’ rather than objective and FAIR CONSIDERATION of what I have already answered to such questions before.

How often have self-appointed ‘experts’ of one sort or another told a ‘crank’ or whomever something to the effect: “It may not be the answer you wanted, but it’s the only answer you are going to get; and just because you don’t understand or don’t like it, tough!”

The latest example of this sort of elitist/double standard was from Trippy, in the associated "1 is 0.9999999999999............" thread in Alternative Theories section:

You not liking it does not invalidate it.

So, James, am I going to be banned for NOT ANSWERING HOW YOU WANTED OR LIKED ME TOO? I trust not, for I can say with equal justification as Trippy et al apply: “Just because YOU don’t like my answers or haven’t understood the posts/information already covered here, its YOUR problem not mine.” Fair ‘nough, James?

Never mind, though, it’s just the sort of ‘strangeness’ that creeps into any situation where people get ‘all steamed up’ about things because they are so convinced they are right because their circuitously based and argued/’proofed’ philosophy-based, unreal-Axioms-derived, ‘math system’ tells them they are right, despite all the self-evident reality-based observations to the contrary to which these same mathematicians are deaf while they repeat obviously (as demonstrated by reality based logics and arguments already) flawed and incomplete and self-referential ‘statements and claims’ which haven’t YET been ‘proofed’ via any INDEPENDENT REALITY BASED arguments/axioms. But you keep deriding and evading and threatening banning etc OTHERS who keep telling you what you don’t want to hear, while your own arguments are demonstrably and repetitively trivial and beside the point being made to YOU.

James, why should I or anyone else even bother playing the ‘unreal/uncomplete math game’ back at you when I have already given you and arfa, Trippy et al the whys and wherefores your math game is based in unreality and philosophy instead of any reality/sane logics/arguments/outputs?

James, it would help you be less ‘emotionally attached’ to patently incomplete orthodoxy, and more objectively placed to objectively LISTEN to what is being SAID in this thread ALREADY which has given you the answers ALREADY to those trivial ‘examples/exercise’ which you and certain others keep insensibly repeating ad nauseam while missing what had ALREADY ADDRESSED those same, and demonstrated them to be IRRELEVANT and/or CIRCUITOUS.

Look, James, arfa, I already explained to Trippy that all these 1/3 etc TRIVIAL manipulations, constructions/deconstructions of symbolic terms are NOT ‘proof’ of anything at all EXCEPT the notation/convention used and NOTHING ELSE. They are NOT any actual process/operation completed, they are ASPIRATIONAL STATEMENTS at best, and misleading assumptions at worst (since in many cases the implied operation is never actually started let alone completed to IDENTIFY EXACTLY what those 1/3 etc expressions actually evaluate to EXACTLY. Just claiming that they DO ‘represent SOME NUMBER YET TO BE ACTUALLY IN EVIDENCE independent of expectations and asssumptions, is NOT PROOF of ANYTHING but those assumptions and expectations which are YET to come to identifiable REAL THINGS and not just some things in an UNREAL math construct from PHILOSOPHICAL abstractions from its starting premises/axioms of ‘dimensionless points’ etc.

James, to get a fuller idea of what my consistent stance is regarding those ‘proofs’ offered up that are, when taken to their very ‘roots’, TRIVIAL and meaningles in any INDEPENDENT sense, you may like to refer to the exchanges between me and Trippy/arfa here and in the other “1 is 0.999...” thread/discussions, for example:

post #1595 where I stressed:

Undefined to arfa said:

It's not that 1/1 is a problem per se. The axioms are ok with that (until the like/like of 0/0 rears its ugly head and the axioms fail....hence my reservations where the arguments/proofs depend on such like/like constructions as crucial to the 'proof' argument.

What I am trying to say is that, just as the LIMITS approach avoids the need for any such 1/1, 9/9, etc trivial and un-elucidating 'devices/exercises’, I am looking for an equally 'non-trivial' way of getting to the same point but not using the unitary/trivial 'devices' mentioned. A way of starting from the fractional string itself and making logical actions/assumptions about it such that the mathematical 'transition' from fractional infinite string to 'unitary' is achieved without the use of trivial 1/1, 9/9 etc manipulations which only introduce what I observe as a bias to the argument/treatment which gives the result you want but is not in the same 'triviality independent' limits method. That's all. I am looking for such a way so that no arguments can be 'faulted' for any reason....**especially for the reason that using axiomatic trivialities such as 1/1 is not a 'complete' approach since the axioms break down when 0/0 comes along.** That's it. Good luck.

...and, James, as another example, my #1666 to origin:

Undefined said:

Hi origin.

Please read my post to Trippy above; it again shows what subtleties you missed (ie, that no division was involved in 1/3 until the operation results in an identifiable number as such (and not just a convenient notational 'unending string', etc etc).

I won't be around much, especially posting, for a while. I'm sure you will celebrate that! Have fun!

Anyhow, good luck and good thinking; and enjoy your polite discussions. See/read you round!

...where I alluded to the points/subtleties he missed in my exchange with Trippy ending at post #1665:

Undefined said:

Exactly, there is no division involved. That is what I tried to explain to origin but he prefers to ridicule rather than try to understand the subtleties under discussion.

Anyhow, as to your exercise per se, I already explained that merely making symbols for things is not actually identifying/proving them as numbers/strings in a fractional state, now is it? Especially if that state is not YET (as you agreed above) identified by actual division operation/process. Yes? That was my point. Mere trivial constructions/de-constructions based on symbolic 'definitions' of multi-unitary 'composite unitary' symbol/set is not actually proving the identity/behaviour of the fractional number/string in the first instance, is it?

**The issue is not the division, as we agreed above it is not yet involved; it is the AXIOMS regarding zero treatment according to those axioms; which axioms treat like/like constructions (such as 3/3, 8/8, 9/9 etc) as UNITARY as per the definitions. When that like/like construction comes to the example of 0/0, then we have a problem. IF that 0 is a number on the number line, then it has a VALUE on the number line as a POINT on that line. Yes? If we have any LIKE POINT/LIKE POINT 'value' then they are equal' and so the expression of 0/0 should be UNITARY also, just like all the others.**

BUT as you now bring in the REALITY into the maths (which I have been trying to do all this time), we find that the 0/0 is a NON-action at best, and an axiomatic quandary at worst. Which is why mathematicians who do NOT resort to Reality to inform the axiom will have no choice in the matter but to call it "axiomatically undefined", since they have no other way to 'handle' that 0 as a number/value under the like/like contexts. Naturally I have the change to the axioms needed for 0 to be consistently treated without such "undefined" situations arising at all. I will be publishing that too soon.

The other aspect of 0 as a placeholder is already evident in the NOTATION convention which leas to all the problems of expressing symbolically a 'something' which is not YET a 'result' of any 'division' that has been 'completed'; let alone any division which has yet to BE started when we use the 1/3 symbol for what we WANT to do but have not YET done UNTIL we 'generate' the conventional notation FRACTIONAL string of 0.333... which we call 'a number/point' on the number line BUT have not yet done anything more than 'equate' 1/3=0.333... AS A NOTATIONAL STATEMENT rather than a true 'complete' mathematical process on EITHER/BOTH sides of that purely notational '=' sign.

These are the subtle aspects which get lost in the cross-purpose exchanges where things YET to be 'done' are ASSUMED 'already done'. So I will leave it at that and leave you with the last word on our exchanges on these matters, Trippy, everyone.

Anyhow, thanks again for all your trouble and courteous contributions to these discussions, Trippy, everyone. I have all I need to finish my complete and consistent, reality-inter-connected 'contextual maths and physics' theory/publication. I will say everything I have to say on this and other matters in that. Until then, cheers to all genuine seekers of scientific and mathematical reality-contextual understandings!

I probably won't be posting again for many weeks. So thanks again and good luck and good thinking to you all.

PS: By the way, Trippy, everyone; just for your information I have 'demolished' the 'Hilbert Hotel' device for 'explaining' infinity and its so-called 'properties' in the context currently being applied/manipulated by the maths. Reality has come to the rescue again to make sense of it all! Oh, and I also have identified what the 'infinitesimal' really is in reality (so QQ will be pleased to have the answer to his Zeno Paradoxes and his 'Reducing Sphere' exercises!). It will all be in my book under the Physics/Maths 'loose ends' section.

...where, James, you will see that once Trippy and I were on the ‘same page’ of REALITY, we agreed on my observations regarding the current axioms/maths results and ‘proofs’ are NOT INDEPENENT from the Unreal starting axioms/philosophy notions, and hence cannot be said that all ‘proofs’ so far presented have any independent thing to say on the matter when the VERY STARTING POINT of the current maths is in question as HERE.

So, James, everyone, it is STILL the case that no repetition and demands from ‘current unreal maths’ can be ‘answered’ PROPERLY except by INDEPENDENT perspectives/answers which do NOT depend on the unreal circuitous ‘current maths answers/demands’ TRYING TO SHAPE AND CONSTRAIN the discussion/answers to “what is acceptable to current maths” which has been already well shown NOT to be comnplete and hence IN NO POSITION to LIKE or DEMAND anything when it is the INDEPENDENT answers that matter in the final analysis/review going on here and elsewhere IN REALITY TERMS starting premises rather than dead-end unreality philosohical starting terms.

The upshot, James? You may not ‘like’ the answers’ and reality observations; and you may not ‘understand’ them using your self-constrained trivial, circuitous, unreal abstractions logic train ‘outputs’ and ‘assumptions’ flowing from an INADEQUATE starting point of ‘dimensionless point’ etc, but that’s NOT MY PROBLEM, now is it? It’s obviously a case like that where all the ‘experts’ basically say to those who would disagree with them and point out where the arguments support that disagreement, and YET those experts default to “Like it or lump it, because you just don’t understand it!” What’s good for the goose is good for the gander when it comes to THIS present situation, obviously. Yes?

Anyhow, I haven’t time to go over old ground when others haven’t bothered to read what has been already said and settled that would give context to why my answer to you now, James, is what it is, because it cannot be anything else in reality. I leave you and others, especially those emotionally-attached-to-unreal-maths GLIB RESPONSES and TRIVIAL ‘proofs’ of nothing real at all, to ponder all the points made without kneejerking to inculcated defense positions which do NOT really address/allow for the new challenges to the vvery basis for those ingrained ‘unreal’ positions. Good luck, everyone...and play nice irrespective of which ‘sides’ you think you are ‘on’. OK?

PS: one can ban people for giving answers one doesn’t ‘like’ or ‘understand’, but that’s not ‘playing criket’ fairly, is it? And it leaves you in your unreal world-of-abstract-maths just that much longer while the realist maths evolution/advances passes you by. Good luck with that, whoever ‘unreality expert’ you may be! No hard feeling from either ‘sides’ I trust!

**Consider what the THINKING mathematicians themselves have already realized. Apart from the TRIVIALITY of proffered ‘formal proofs’ so far from conventional maths contruct, ***there is the inescapable fact as Goedel and others have recognized for some time now:*__ One cannot use arguments from WITHIN an abstract philosophical/maths construct to ‘prove’ anything about that same construct; because such proffered ‘proofs’ are NOT INDEPENDENT, but inescapably, circuitously self-referential.__
Get it now?

**The ONLY INDEPENDENT system is the REALITY; and that is the ONLY FINAL ARBITER construct from within which REAL PROOFS ARE POSSIBLE that are not circuitous and self-referential, BECAUSE there is no abstraction involved, since the objective physical reality is ALL THERE IS and IS intrinsically, logically, physically and demonstrably COMPLETE and CONSISTENT irrespective of any partial/incomplete abstract ‘takes’ from it by unreal philosophical/maths modeling by us.**