# 1=0.999... infinities and box of chocolates..Phliosophy of Math...

Divide a pizza made of 100 atoms by 3 equal pieces?
That's because you start with something that is physical that is necessarily indivisible.
Maths is not physical.
You are applying limitations that simply do not exist within maths.

Just try your same argument with 300 atoms, or $300. According to your argument if you gave 3 people$100 each and then took it back, you'd be left with less than you started.
(Maybe that's how the banks make their money! )

Why would your argument hold for $100 but not$300?

You need to stop looking at real world examples as a means of disproving maths.

0.999 + 0.999 = 1.998
$$\left( \sum_{k=1}^n \frac{9}{10^k} \right) + \left( \sum_{k=1}^n \frac{9}{10^k} \right) = \dots = 1 + \left( \sum_{k=1}^{n-1} \frac{9}{10^k} \right) + \frac{8}{10^n}$$
So for n=3
0.999 + 0.999 = 1.998
0.999... + 0.999... = 1.999...8
$$\left( \sum_{k\geq 1} \frac{9}{10^k} \right) + \left( \sum_{k\geq 1} \frac{9}{10^k} \right) = \dots = 1 + \left( \sum_{k\geq 1} \frac{9}{10^k} \right)$$

So for never-ending repeating decimals, 0.999... + 0.999... = 1.999...

Never-ending sums have qualitative differences from sums with just a finite number of terms.
If 0.999... = 1 then
0.888... = ?
0.777... = ?
0.666....= ?
0.555... = ?
etc???

fill in the ?'s
By virtue of the cyclic nature of the state in the division algorithm #2, it follows in base 10 that:
$$\begin{eqnarray} 0.999... & = & \frac{9}{9} = 1 \\ 0.888... & = & \frac{8}{9} \\ 0.777... & = & \frac{7}{9} \\ 0.666... & = & \frac{6}{9} = \frac{2}{3} \\ 0.555... & = & \frac{5}{9}\\ 0.444... & = & \frac{4}{9}\\ 0.333... & = & \frac{3}{9} = \frac{1}{3} \\ 0.222... & = & \frac{2}{9}\\ 0.111... & = & \frac{1}{9}\\ 0.000... & = & \frac{0}{9} = 0 \end{eqnarray}$$

Division algorithm 2 for positive rationals
Let $$s'_0 = ( p \; \textrm{mod} \; q ) + q \left[ q|p \; \wedge \; p \neq 0 \right] , \quad a'_0 = \frac{ p - s'_0 }{q}, z'_0 = a'_0$$ then it follows that $$a'_0 \in N_0, \; s'_0 \in N_0 \; s'_0 \leq q, \; z'_0 = \sum_{k=0}^{0} b^{-k} a'_k , \; b^0 p = s'_0 + b^0 q z'_0$$
Let $$s'_{n+1} = \left( (b s'_n) \; \textrm{mod} \; q \right) + q \left[ q|(b s'_n) \; \wedge \; s'_n \neq 0 \right] , \quad a'_{n+1} = \frac{ b s'_n - s'_{n+1} }{q}$$ then it follows that $$a'_0 \in \mathbb{N}_0, \; s'_0 \in \mathbb{N}_0 \; s'_{n+1} \leq q, \; a'_{n+1} < b, \; z'_{n+1} = \sum_{k=0}^{n+1} b^{-k} a'_k , \; b^{n+1} p = s'_{n+1} + b^{n+1} q z'_{n+1}$$
If you say that 0.999... = 1 then you are saying
0.888... = 0.888...9
I would never say something like that because that notation says there is a last digit in a never ending sequence of digits.

@ Bds,
Maybe this will help;
Do you think that in mathematics, 0.999... = 1 means that the 0.999... sequence terminates at 1
If so why?

Maths is not physical.

Then it can't be used for physics, because physics is physical. If math is not compatible with being physical, then you can not use it in physics. Are you really that....

Then it can't be used for physics, because physics is physical. If math is not compatible with being physical, then you can not use it in physics. Are you really that....
I didn't say it wasn't compatible.
I said that it isn't physical.
You can abstract things in maths that you can't do in the physical world.
You can not create a perfect sphere in the physical world.
You can not have an actual negative quantity in the physical world (I've always imagined what -1 litres of water looks like).
You can not split a pizza into an infinite number of pieces in the physical world.
All these things you can do in the abstract realm of mathematics.

Maths helps us model and understand the physical world.
Yet maths is not bound by the limitations of the physical world, but by its own inherent structure.

So while the physical world adheres to a subset of what mathematics can describe, mathematics is not bound to what is possible in the physical world.
Your argument is a logically fallacy, as already pointed out previously, as you affirming the consequent.

The same goes for everyone. I'm not gonna waste my time playing musical chairs with you. Show me that you are smart enough to understand what is done in that diagram. Show me that you're an honest person, and not some religious fanatic sticking to your pseudo scientific beliefs. SHOW ME!

Why are you changing the subject?

That's a troll tactic, and you know it.

This thread is about 0.999... = 1. Stay on topic.

We've discussed your silly box to death in previous threads. It's as wrong now as it was 3 years ago, and for the same reasons I gave you back then. (*)

BdS:

If you say that 0.999... = 1 then you are saying
0.888... = 0.888...9
0777... = 0.777...8
0.666... = 0.666...7
0.555... = 0.555...6
etc...

No, because the statement 0.999... = 1 is true, whereas the other statements you have here are wrong - in fact, meaningless. I already explained to you: you can't tack on a digit at the end of those three dots. They mean the sequence of digits repeats forever. There's no end to it, so there's no end to which you can tack on an extra digit.

Also, rpenner already pointed out the simple fact that:

0.999... = 9/9 = 1
0.555... = 5/9
0.111... = 1/9

etc.

If you dispute the correctness of this (and this applies equally to Motor Daddy), then tell me what you think the correct decimal expansion of one-ninth is, or one-third, or one-seventh for that matter.

---
* Maybe it wasn't 3 years. Maybe it was 1 year. Anyway, it was done.

For what purpose do you define the family $$T_n$$? $$S_n$$ exists so I can more easily say "for every counting number, n, the statement $$S_n \lt S$$ is true" without the clutter of a bunch of complicated symbols that are subject to typos.

But what is the special utility of $$T_n$$ (as $$\frac{9}{10^n}$$ is pretty concise and typo-resistant)?

Another thing that is true is for every counting number, n, is "$$S_n + \frac{1}{9} T_n = 1$$."

This is precisely the reason why i am using the term $$T_n$$. From the above equation it can be seen that $$T_n = 9 \times (1 - S_n)$$.

In other words, any positive number is more than some (or all!) members of the family $$T_n$$.

Yes, that is true in analysis and non-standard analysis (a subject which I recently read up on).

No, because $$T_n$$ isn't a number, it's a family of numbers and doesn't have a specific value until you specify what the counting number n is. By itself, $$T_n$$ is just a convenient way to talk about the whole family or some abstractly specified member of the family.

An there is no value of n which makes $$T_n = 9 \times 10^{-n} = 0$$ true, because $$T_n$$ is only defined for the counting numbers.
There are an infinite number of members of that family, one for each of the counting numbers, but all are positive, which is to say, greater than zero.

What is correct to write is $$\lim_{n \to \infty} T_n = 0$$ which builds on the previous observation that "any positive number is more than some (or all!) members of the family $$T_n$$. "

I was implying this only in my previous post, thats why i mentioned "In that case... (implying $$n \to \infty$$)".

-- Specifically it is saying for any positive number, there is a finite number, m, so that every member of the family $$T_n$$ where $$n \gt m$$ is closer to 0 than that chosen positive number. And since no matter how large m is, most counting number are larger than m, this means no matter how much you "zoom in" on 0 with a microscope, there are still an infinite number of the family of $$T_n$$ close to it.

Limits and suprema are two topics of analysis that follow from the properties of real numbers which in turn follow from the basic geometrical ideas that Euclid wrote about.

I don't know what this means, but I think you haven't yet understood the notation and reasoning of my earlier post.

Consider $$T_n = 9 \times (1 - S_n)$$. Also $$S_n = \sum_{k=1}^n T_k$$. Here $$T_n$$ is the $$n$$-th term of the geometric series of $$S_n$$. Here $$n$$ is the counting number as defined by you.

You also considered $$S = \lim_{n\to \infty} S_n = 1$$. So, $$\lim_{ n \to \infty} T_n = 9 \times (1 - S) = 9 \times (1 - 1) = 0$$.

But $$T_n$$ being a term of the geometric series can not be $$0$$.

Hence, there is a flaw in your proof that $$S = 1 = 0.999...$$

No member of the $$S_n$$ family is equal to a sum over more than a finite number of terms. In short, $$S_n = \sum_{k=1}^n T_k$$. However $$S$$ is equal to a sum over all members of the $$T_n$$ family and thus equal to a sum over more than any finite number of terms. $$S = \sum_{k \geq 1} T_k = \sum_{n \in \mathbb{N}} T_n = \lim_{n\to \infty} S_n = 1 - \lim_{n\to \infty} 10^{-n} = 1$$. But $$S$$, just like 0.999... and 1, is just a name for a number.

And it is the properties of numbers (specifically the completeness of the real numbers and the property of the counting numbers to go on forever) that are the main points of disagreement in this thread, even though these are mathematical properties that follow directly from the relevant definitions.

I don't think Hansda understood this argument, because there wasn't an question or disagreement with a particular part of the argument, but a denial of the conclusion. That's no basis for a meeting of the minds.
And for every n greater than or equal to 1, we can prove $$S_{n+1} = S_n + \frac{9}{10^{n+1}}$$ and $$\frac{9}{10^{n+1}} \gt 0$$ so $$S_{n+1} \gt S_n$$.
So presumably $$S_1 \lt S_2 \lt S_3 \lt \dots \lt S_{n+5}\lt S_{n+6}\lt S_{n+7} \lt \dots \lt S$$ and indeed this is provable from the rules of inequalities.
So any member of the family of $$S_n$$ is less than $$S$$, in other words each member is a lower bound on what the value of $$S$$ could be. But none is the greatest possible lower bound on what $$S$$ could be.
... I now know that $$S_n = \frac{9}{10} \times \frac{1 - 10^{-n}}{1 - 10^{-1}}$$ is true for all counting numbers, n.
But because $$\frac{9}{10} = 1 - 10^{-1}$$ this also proves that $$S_n = 1 - 10^{-n}$$ for all counting numbers, $$n$$.

Thus our lower bounds on what $$S$$ can be looks like this:
$$1 - 10^{-1} \, \lt \, 1 - 10^{-2} \, \lt \, 1 - 10^{-3} \, \lt \dots \lt \,1 - 10^{-(n+5)} \, \lt \, 1 - 10^{-(n+6)} \, \lt \, 1 - 10^{-(n+7)} \, \lt \dots \lt S$$

Now I want to prove that if $$X$$ is less than 1 then there are members of the family $$S_n$$ which are larger than it.
Say $$X \lt 1$$. Then $$0 \lt 1 - X$$. Then $$1 - X$$ is a positive number. Then there is a real number $$\epsilon$$ such that $$e^{-\epsilon} = 1 - X$$ because $$f(x) = e^x$$ is a continuous function takes on all positive real values. Also $$f(x \ln 10) = e^{x \ln 10} = 10^x$$. So $$X = 1 - e^{-\epsilon} = 1 - 10^{- \frac{\epsilon}{\ln 10}}$$. So the question of if there are members of the family $$S_n$$ which are greater than $$X$$ reduces to the question of asking if there are counting numbers which are larger than the real number $$- \frac{\epsilon}{\ln 10} = - \frac{\ln ( 1 - X) }{\ln 10}$$ and the answer is yes, most of them.
So every number less than 1 is less than some (or all!) members of the family $$S_n$$ and thus less than $$S$$.

Thus 1 is greatest lower bound on what S could be, because all numbers less than 1 fail to qualify.

One of the biggest principles of the real numbers is that if a non-empty set of numbers has a upper (or lower!) bound then it has a least upper bound (or a greatest lower bound). By this, we see that the set of positive rational numbers whose square is less than 2 has greatest lower bound of 0 and a least upper bound of √2. 0 is not positive and √2 is not rational, but they are the minimal bounds of that particular set of positive rationals. That's why $$S$$ which is the least upper bound of the family of $$S_n$$ need not be a member of the family and can be 1.

Likewise $$\lim_{n \to \infty} S_n = \lim_{n \to \infty} (1 - 10^{-n}) = 1 - \lim_{n \to \infty} 10^{-n} = 1$$ provides a concise line of reasoning for what S is.
Having established that no number less than 1 could be an upper bound of the family $$S_n$$ and having established that the family $$S_n$$ is strictly increasing with each successive value larger than all those previous, I came to the conclusion that the only possible value of $$\lim_{n \to \infty} S_n$$ is 1.
Identically, if I were to establish that no number greater than 0 (no positive number) could be a lower bound of the family $$10^{-n}$$ and also establish that the family $$10^{-n}$$ is strictly decreasing, then I would come to the conclusion that the only possible value of $$\lim_{n \to \infty} 10^{-n}$$ is 0.

So every number less than 1 is less than some (or all!) members of the family $$S_n$$ and thus less than $$S$$.
Thus 1 is greatest lower bound on what S could be, because all numbers less than 1 fail to qualify.
In other words, any positive number is more than some (or all!) members of the family $$T_n$$.
Just as I considered $$\lim_{n \to \infty} 10^{-n}$$ briefly in the first post, so did I consider the lower bound of the family $$T_n$$ and the value of $$\lim_{n \to \infty} T_n$$ in the second post.
An[d] there is no value of n which makes $$T_n = 9 \times 10^{-n} = 0$$ true, because $$T_n$$ is only defined for the counting numbers.
There are an infinite number of members of that family, one for each of the counting numbers, but all are positive, which is to say, greater than zero.

What is correct to write is $$\lim_{n \to \infty} T_n = 0$$ which builds on the previous observation that "any positive number is more than some (or all!) members of the family $$T_n$$. " -- Specifically it is saying for any positive number, there is a finite number, m, so that every member of the family $$T_n$$ where $$n \gt m$$ is closer to 0 than that chosen positive number. And since no matter how large m is, most counting number are larger than m, this means no matter how much you "zoom in" on 0 with a microscope, there are still an infinite number of the family of $$T_n$$ close to it.

Limits and suprema are two topics of analysis that follow from the properties of real numbers which in turn follow from the basic geometrical ideas that Euclid wrote about.

So, $$\lim_{ n \to \infty} T_n = 9 \times (1 - S) = 9 \times (1 - 1) = 0$$.
Correct! In fact I said this myself before.
But $$T_n$$ being a term of the geometric series can not be $$0$$.
I never said there was a value of n that made $$T_n$$ equal to zero. I already said there is no value of $$S_n$$ that equals 1 -- but that's not surprising because there also is no member of $$S_n$$ that equals $$S$$ and the value of $$S$$ is the point of this whole thread. All members of the family $$T_n$$ are positive. But if you name any positive number, no matter how small, then most of the family $$T_n$$ are going to smaller than that positive number. So no positive number can be a lower bound on the family of $$T_n$$. Thus 0 is the greatest possible lower bound on the family of numbers $$T_n$$ and no matter how small any particular $$T_n$$ might be all further values ( $$T_{n+1}, T_{n+2}, T_{n+3}, \dots$$ ) must be smaller still. Thus 0 is also the value that the sequence $$T_n$$ approaches for arbitrarily large values of n. And the way you write this is $$\lim_{n \to \infty} T_n = 0$$.
Hence, there is a flaw in your proof that $$S = 1 = 0.999...$$
I believe all that you have done was to demonstrate that you didn't understand my last two posts on the subject of limits. If you understood the argument then you would either be able to tell me what the specific flaw is or have a specific question about some part of the argument you didn't understand. Instead you deny the consequence of the argument without specific objections. Instead of objecting to parts of my argument you simply rephrase points I had already made.

Do you think that in mathematics, 0.999... = 1 means that the 0.999... sequence terminates at 1

no I keep looking at 0.999... and thinking something is missing to make it equal 1

By virtue of the cyclic nature of the state in the division algorithm #2, it follows in base 10 that:

I think the problem might be here. Do you count 0 as a number? Is there another 10 base that goes from 1 - 10 and not 0 - 9?

Do you count 0 as a number?
Yes, of course I do. If zero was not a number then $$3 - 3$$ is not a number and all of subtraction breaks. Likewise $$10 + (-3) + (-7)$$ shows addition of negative numbers breaks.
Is there another 10 base that goes from 1 - 10 and not 0 - 9?
Then you could not concisely express a fraction less than $$\frac{1}{9}$$ because the smallest never-ending decimal is $$\sum_{k \geq 1} \frac{1}{10^k} = \frac{1}{9}$$ and the smallest terminating fraction is $$.1 = \frac{1}{10}$$.

That sorts my understanding out. I wasn't seeing the 9 as the upper bound I was thinking it was 10. Thats why I was trying to add the extra digit to get 0's. Thanks for your time and patience

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.

1 day=100%. 24 hours=2,400%

We are dividing 100% into pieces, not 2,400% into pieces.
100% of 1 day is 24 hours.

Wrong. We are not dividing 24 hours into piles of hours, we are dividing days into piles of days.
Yes. I divided 1 day into 3 piles of third-of-a-day.

One-third of a day is 8 hours.

Do you agree?

If not, how long is a third of a day?

Or do you think that it's meaningless to speak of a third of a day?

Can you have half a day? How long would that be? What about one-tenth of a day? Is that possible?

Any ideas how long half a day would be, Motor Daddy?

I conclude that you've never understood a word of math, since 1st grade.

You're woefully equipped to judge such things. Previously, you admitted you couldn't understand post #915, above. And you have no response to my post about the representation of fractions such as one-third in bases other than decimal.

In fact, you seem to ignore almost all of the substantive arguments I put to you.

Are you really this stupid, or is this all just a ploy to pass the time?

James, if you have read enough of the background arguments (especially my latest post to you above), you should by now understand why such ‘exercises’ have no real independent logics to them, but only self-assumed statements of assumptions, ad infinitum from the starting unreal assumptions.

Can’t you ‘get’ that Motor Daddy has ALREADY pointed out to you that the TRIVIAL CONSTRUCTION and equally TRIVIAL DEconstruction exercise is VERBOTTEN from first principles? Mere construction of a COMPOSITE UNITARY from OTHER INDIVISIBLE UNITARY identities is a PHILOSOPHICAL HEIRARCHICAL CONCEPTUAL exercise and NOT a mathematical/logical PROCEDURE that proves anything like what youn WANT it desperately to ‘prove’?

The division can be of some EVEN CONTRUCTED UNITARY OR an ODD UNITARY. The ODD unitary is the CLOSEST concept/entity to the minimal quantum unitary INDIVISIBLR unit of effectiveness, be that infinitesimal effectiveness quanta in maths or physics context.

It all STARTS from that, and any further operations can be trivial or meaningful depending on the exercise and the unitary involved. For example YOU have DECONTRUCTED “1” DAY into 24 hours, thus EFFECTIVELY converting an ODD unitary into a number of EVEN UNITARIES SUB-UNITS. So naturally that TRIVIAL exercise will suit that trivial purpose, but it does not ‘prove’ anything, nor can you base any conclusions at all on it, because it IS trivial and SELF-SELECTIVE in the construction which will ‘output’ whatever YOU built into it ARBITRARILY and TRIVIALLY.

That’s what my previously referenced discussion with Tippy pointed out. Ok?

You have to treat the REAL NON-TRIVIAL CASE of 1/3, as the essentially ‘boiled down’ expression that shows you CANNOT trivially manipulate that expression any further by making the numbers EVEN case as you tried with the 24 hours in the ONE unitary day etc.

PS: To both James R and Motor Daddy equally:

I have bolded those sentences in James R’s and MD’s posts quoted above. I must STRONGLY OBJECT to ANYONE in ‘authority’ OR ‘ordinary’ member status, making such obviously personal and prejudicial innuendos about anyone, ok James, MD?

Having said that, it is especially tragic and galling because so far the only person(s) in these discussions who HAVEN’T LISTENED OR UNDERSTOOD PROPERLY what was being pointed out to them is the ‘maths responders’ defaulting AGAIN and AGAIN to trivial, repetitive, self-selected ‘chestnut arguments/proofs’ which (IF they had been listening and understanding properly) have already been shown to BE trivial and INCOMPLETE and hence not valid as INDEPENDENT arguments/proofs, because they don’t cover ALL physical cases, real and/or unreal. They never will or can be valid or independent, because, as Goedel et al have shown, those arguments/proofs from WITHIN that maths-philosophy based ABSTRACT construct cannot ever represent anything other tha self-referential trivialities where PROOFS OF THE STARTING AXIOMS cannot be had, nor their consequent conclusions.

Once these personal insults start flying, it makes both ‘sides’ feel ‘justified’ in just insulting and stop listening to each other. So PLEASE, for the sake of science and this forum, everyone, stop insulting. Especially if yt’s just a case of you not liking or not understand what is being pointed out that is BEYOND the LIMITED capabilities of the current maths-philosophy abstract construct where ‘proofs’ of anything real and externally indepedndently consistent is required ABSOLUTELY if anything is to be ‘proven’ at all that makes sense FROM REALITY PERSPECTIVE ITSELF.

Take a breather, everyone; and re-read all the discussions here and elsewhere properly and without kneejerking and crank/elitist ‘deafness’ and ‘biased interpretations’ etc. Just follow the bouncing ball of reality arguments and points, and only then make up your mind on what the only conclusions can be in this review of ‘current maths axioms’ and construct in the light of objective reality. Good luck!

Hi arfa, James, everyone.

It is timely to point out that the phrase: You can’t get THERE from here”, and “You can’t get BACK HERE from THERE”, are quite seriously apt to illustrate where all your and others current mathematical ‘trips’ are NON-STARTER and/or NON-SEQUITURS from any ‘LIMITS based false starts ’ you imagine when you just write down 0.999..., 1/3 etc as if they identify anything real at all.

Consider: When dealing with an ACTUAL UNITARY and not a trivially constructed/deconstructible unitary entity...

Merely invoking philosophical INFINITY concept does NOT actually ‘get you there’ from 1/3, or 1/9 etc , because you never can, hence the 0.333..., 0.111... etc.

Nor can you ever ‘commutate’ backwards from infinity of 1/2+1/4+... back to 1 unitary, since you NEVER WERE AT INFINITY to ‘start back from’.

If you can just stop and think clearly and dispassionately for a moment what all your trivial/abstract exercises and construction/deconstructions ASSUME INCORRECTLY in that area of ‘getting therre and back’ from ‘philosophical/unreal infinity’ concept/limits treatments etc, then you may get an inkling where the current maths DOES inevitably hit the brick wall of reality eventually....where the ultimate infinitesimal of effectiveness QUANTUM UNITARY ENTITY exists at both ends of the physical/logical scale (ie, the infinitesimally smallest quantum EFFECTIVENESS ‘singularity state’; and the infinitely largest COMPOSITE quantum of EFFECTIVENESS ‘singularity state’).

All else is philosophy and window dressing abstractions/assumptions which doom such as the current unreality/philosophy based maths/physics models to INCOMPLETENESS and unlimate self-referential illogics when reality comes knocking!

Take care and take note also of all that which you may not like or understand but you cannot deny in reality, folks!

Hi Baldeee.

Then it can't be used for physics, because physics is physical. If math is not compatible with being physical, then you can not use it in physics. Are you really that....

I didn't say it wasn't compatible.
I said that it isn't physical.
You can abstract things in maths that you can't do in the physical world.
You can not create a perfect sphere in the physical world.
You can not have an actual negative quantity in the physical world (I've always imagined what -1 litres of water looks like).
You can not split a pizza into an infinite number of pieces in the physical world.
All these things you can do in the abstract realm of mathematics.

Maths helps us model and understand the physical world.
Yet maths is not bound by the limitations of the physical world, but by its own inherent structure.

So while the physical world adheres to a subset of what mathematics can describe, mathematics is not bound to what is possible in the physical world.
Your argument is a logically fallacy, as already pointed out previously, as you affirming the consequent.

Unless your ‘unreal maths’ PROOFS covers ALL possible instances/formulations of the ‘problem/concept’, then it is NO PROOF of anything except ‘special unreal cases’ which are self-referenctial and trivial therefore, because they only ‘satisfy’ the unreal boundary conditions YOU put by trying to EXCLUDE those REAL PHYSICAL cases where your ‘unreal’ maths ‘proof’ OBVIOUSLY BREAKS DOWN.

So, in reality, the ‘proof/exclusion’ shoe is on the other foot than the one you tried to convince MD and others here it was on. Yes?

BdS said:
Do you count 0 as a number?

Yes, of course I do. If zero was not a number then $$3 - 3$$ is not a number and all of subtraction breaks. Likewise $$10 + (-3) + (-7)$$ shows addition of negative numbers breaks.
No, it just means you have to fix the Axioms/definitions so that 0 is a number ON the number line and 0/0 is NOT undefined etc. Else you ignored that on the number negative-0-positive number line the 0 is an ORIGIN of BOTH ‘legs’, negative and positive, and hence is a ‘superposition/transition’ entity/concept, not a simple number. Until you fix it you’ll get all these sophist ad hoc self-referential ‘proofs’ and ‘tricks’ which sidestep the actual problem with the current axioms/consequential arguments and outputs etc.

BdS said:
Is there another 10 base that goes from 1 - 10 and not 0 - 9?
Then you could not concisely express a fraction less than $$\frac{1}{9}$$ because the smallest never-ending decimal is $$\sum_{k \geq 1} \frac{1}{10^k} = \frac{1}{9}$$ and the smallest terminating fraction is $$.1 = \frac{1}{10}$$.

If we fixed the Axiomatic starting point problem regarding 0 (see my previous posts above), then all these ifs and buts would not arise at all; and all these sophist ‘fixes’ and ‘exceptions’ and ‘straightjacketing’ ILlogics would not require all these esoteric and unnecessary ‘dimensionless point’ etc complicating abstractions/gymnastics. It would simplify everything FROM THE START such that all these professional pursuit of esoteric UNREALITY maths ‘expertise’ would be immediately ‘surplus to requirement’.

Think again before you default to unreal maths to justify the unreal/philosophically based results and contortions you have to ‘invent/overlay ad hocly’ in order ‘non-answer’ simple REALITY based questions asking for real INDEPENDENT proofs and not more self-referential unreal ‘proofs’. Thanks, and good luck!

Last edited:
Please fix your quotes to have the proper formatting. You have mangled them pretty badly in places and broken the links back to their original context.

Yes, of course I do. If zero was not a number then $$3 - 3$$ is not a number and all of subtraction breaks.

I'm not disputing your math in your math world, or even that you can prove it to be true. I'm not in any way making this personal, so don't take it that way, but that is insanity! That is absolute insanity!

In my world, zero is a value. We represent that value with the symbol "0."

In my world, "3" is a value. So if you write "3-3=0", to me that is saying, I started with 3 apples, and the dog ate all of them.

Please fix your quotes to have the proper formatting. You have mangled them pretty badly in places and broken the links back to their original context.

I copied text straight off the page while still not allowed to log in, so the LaTex etc got mangled. Now fixed. Thanks.

But no matter, the LaTex is great but irrelevant in light of what I pointed out about all the unreal' and philosophy rooted LaTex 'presentation/proofs' involving ultimately pointless (in the context of this discussion) equations/assumptions etc, as per my previous observations.

It would help the discussion avoid more aggro from more cross-purpose exchanges brought about by people NOT reading and understanding properly what has ALREADY been pointed out that makes all those 'stock answers from unreality maths' MOOT once the reality is checked.

Reality is the ONLY independent construct within which anything can be PROVEN.

No unreality maths system can prove its own unreality-based Axioms (Remember Goedel!).

That is the point, and that is the reason for moving EVERYTHING into the reality context so we can at last complete both the physics and the maths together and consistent 'from scratch' and without all the 'undetermined' and 'unknown' gaps in both the maths and physics. Good luck.

I think my Kindergarten teacher's words were something like, "Three take away three equals zero."