And you’re not appreciating the debate by merely stating that .9999… = 1 — this actually creates something of a paradox and is not black and white. The issue with base minus one is that it always causes this paradox and gives the numbers peculiar properties.
As for your post in base 9, it looks like you derived the repeating output for 1/7 through multiplicity… which is actually a really cool discovery.
I have never found 0.999…=1 to be problematic at all. It works for any 9 that goes to infinity, this is just what we mean in mathematics when we say a “limit”. This is an asymptotic curve, it “never reaches 1” but of course in terms of infinities, it practically-speaking does reach 1, is the same as 1.
In terms of the formula and proof of 0.999…=1, we can find the “error” in division by infinity: when we operate to divide by infinity we are committing the “mistake” of treating infinity finitely, which is not so much an error as it translates the results of our operation into finite terms; i.e. “0.99999…” equals “1”. This works conceptually because of the asymptotic limit aspect to .9 barred, a convergence on a specific quantity, but the whole seeming contradiction of stating it as equals 1 arises because we have flattened the infinite term into finite terms when we divided by infinite in that part of the operation of the proof.
Yes it is. And it is thanks to HMIE that I was able to make it.
Furthermore, this is actually demonstrating what we are saying with the base 9 number wheel. 9 is bounded by 8 and 1, such as here,
What we mean when we say “.999 to infinity” is to approach any number from one side absolutely, “forever”. In reality every further increment closer we go without hitting that number is creating a new 9-cycle of numbers, a whole new “number wheel” as the one above. Thus we may wish to go from 4 to 5, we go
4
4.9
4.99
4.999
4.9999
4.99999
4.999999
4.9999999
Etc.
And conceptually-speaking we can do this forever; in that sense, if that is what we intend to mean, then our operation is converging upon 5. Thus “4.999…=5” is perfectly valid and easy to understand.
None of those are true.
You can also see more about this 9-spoked number wheel and the system of numbers as 1~9 (no zero) as we have developed these ideas in my other topic,
You may want to pay particular attention to this following part,
This is how numbers actually work, this is what they are ‘doing’ when we perform mathematical operations on them.
In my example of 7x2 above, “14” simply means “1 and 4” as in “1 full 9/9 cycle, plus an additional 5/9 cycle” (from 9/9 we move forward now 1, 2, 3, 4, 5, five movements up from the 9; this is precisely, mathematically, logically why “14” is 1+4=5). This is literally what we do when we add and multiply numbers by hand, although we don’t actually realize it.
I’m intrigued. And for heavens sakes, don’t call me a troll! I live for stuff like this… This could be a really good idea. But I will clarify!!! If we counted in base 11, you’d find the same theorem in a different form, so don’t get superstitious about numbers on me!!!
You need to demonstrate that with base 11 for me to see what you mean. If you can’t get in “down and dirty” with the numbers then I can’t see you really know what you’re talking about. Granted, what you are saying is not patently irrational, but this is the reason I called you a troll, that you enter into this topic with NO intention of actually engaging the work here that HMIE has done.
I didn’t have any sense for what he was doing with the numbers either, until I actually sat down and tried working through some things. It really takes that kind of effort. All these others flooding his topics have not even bothered engaging the numbers at all, in which case, they are just here for their own psychological self-gratification. One of them happens to be a mod, that goes to show you what this website thinks of itself in terms of honesty and integrity.
Any base number system is “artificial” in the sense that as humans we can construct whatever base system we like and it will follow the same ordered rules, and produce consistent results. But the point is to try and find the best system. Is base 11 better than base 10 or base 9? If you think so, then why? If not, then why are you using it as an example? Is your point to state that “well you could to that in base X whatever else too!” as if that discredits any of the work here? I am sure that “numerology” would appear in any base number system adequately elaborated.
There is a clear reason I have chosen a 9-spoked number wheel (and this isn’t nonary), it is because the common base 10 is all fine and good except that only 1~9 are numbers, while 0 is actually not a number. Thus striking the 0 in terms of how we use the numbers yields a “base 9”, which is actually just the 9-spoked number wheel I showed you above.
Ouch… you made a huge mistake here. You don’t have to use zero to have infinite bases, you just need different symbols. Do you really want me to do his work in base 11? I have a lot on my plate man.
Are you even going to address what I write?
I made no mistake of any such kind, I never assumed that we need a zero to have infinite bases, nor did I say that we can’t use different symbols. OF COURSE we can use different symbols, and OF COURSE we can use “zero” however we like. My point was that we have this common base 10 system that we are familiar with, we have the 1~9 numbers (symbols) that mark clear meanings and quantities we can express and relate to easily.
This isn’t about however many possibly infinite ways we can sub-divide reality into different number base systems. It is about how reality is actually constructed. How many petals does a flower have? How many branches of a tree from the trunk as you move upward? How many spokes sticking out from a snowflake? How many chromosomes in our DNA? How many arms do you have, fingers, senses, organs? How many planets does this solar system have?
These are all objective questions with objective answers. You can call those answers whatever you want, but the fact of that quantity remains the same. We choose to say we have 2 arms because “2” has been developed to mean the quantity we call “two of something”. I shouldn’t even need to be explaining something so basic here.
Look, what matters is the quantities and forms-structures that actually exist in reality. You can’t say that we have a potentially infinite number of arms or chromosomes or senses, because that is false. There are endless possible ways you can choose to EXPRESS the number of arms you have, but that number, that objective quantity, is the same no matter how you choose to talk about it.
And if you want to choose some other base number system than 9 or 10, I am interested to find out why you think it is preferable. So please demonstrate your preferred base number system and why you think we ought to be using it over base 9 or 10.
I don’t have a preferred base, that’s the whole point. You damn well know as well as I do that these theorems can be written in base 11, 12, 1222, etc… You’re not a moron. But for someone to come in here and say 369 is everything is to have very little comprehension of mathematics. You’re talking to the guy who’s been working on isolating consciousness signatures with pure mathematics so we can read each others clusters of thoughts and intents without chips.
I know a little bit about number theory and mathematics. I spent a while just using division of euclidean objects to derive a new form of division… for example, when you use two straight lines you can create 3 objects or 4 objects depending on bisection, when you curve the lines, even more. I read what you posted mechanical… I think it’s cool as hell and I understand it, I even looked into that problem myself for a little bit.
Right, I am glad you enjoy it. The point HMIE is making with 3 6 9, the same point Telsa too made, is regarding the quantities. “Three things” is not a subjective, relative, infinitely plastic thing, it means a very literal, clear and objective quantity. We just use the number-symbol “3” to describe it, but that symbol-number is pointing us to the reality of “three-ness” (without the number or word, in this case a “3”, we have no other way of even talking about that quantity itself).
Do you believe that quantities are objective? Is it objectively true and fixed the quantity of arms you have?
The point I’m trying to make is that this will end up and fractions in other bases… 3 is not so important, I tried to explain that earlier when I explained particle polarity, by that theory 4 is more important, and as James so eloquently stated, USEFUL! Don’t get superstitious about numbers!!!
And yes, when I stated earlier that one has to be more than one, which was just stated in another thread HERE on these boards by someone, you can maleate numbers. I get that I have two arms, I get that we live in an asymmetrical universe where consciousness cannot hold a bound infinity, so I understand that there are patterns. But the most important thing is to not get superstitious about numbers.
I want to make a point about HMIE… I have gone back and read several threads. On a lot of this stuff… it’s just not there. The additive property and the ability to derive repeating rationals from multipliers is about all you have really accomplished with respect to mathematics. I have seen horrible leaps into illogic in those posts.
Another post on this subject… you didn’t actually prove the theorem that finds all the rationals from multipliers, you started with one repeater for 1/7 and ended with it… I know how to reverse engineer it though.
It’s not totally insane to do what you’re doing with numbers… adding them and deriving their lowest common denominator in a base. If it works it works! Your additive property is fascinating.
Three becomes so found and so well known because we think in terms of opposites, poles.
And when you have two poles, you have;
So “3” is found everywhere merely because of how we tend to think of things.
It could be 4 or 5, but that is too complex for the typical homosapian;
It is just the mind playing with itself and finding the patterns derived from its own presumptions, “mathsturbation”.
Past, present and future.
You can have a present-past just by remembering something.
4 is like 5, both are dimensional numbers, 3 is like 1, it perpetuates along a simpler axis.
In the table of integers, 4 and 5 require the whole spectrum to unfold, 3 is a more self-contained logic.
3 and 4 were understood to be ‘possible’ and ‘manifest’
3 is the basic ground, 4 is the basic expanse.
“Three is a crowd” - with 3 we can say there is a quantity - with 3 there can be perspective and a dynamic.
The point is to compute the number 3 as a triangle, the number 4 as a tetrahedron or parallelogram, a 5 with the golden ratio spiral, 6 with carbon, 7 with spectrality, etc.
Quantities are not quantities of ‘goods’, but of points. Specific numbers of positive existences (“points”) bring about possibilities for specific behavioral elements of the universe - as we interpret it.
I do not go as far as to separate numbers from the mind - but this means only that it is ‘the minds way of apprehending objectively’. It it the function of the mind itself, which has every appearance of being a mirror function.
Look at numbers as entities, as beings that constitute the human capacity to compute abstractly. They do not refer to anything other than what they already represent. There is nu ‘flesh behind the veil’, there is only the quantity = degree of of separation which means the possibility for spatial action, mapping, imagining, thinking. One could say the numbers represent the active faculty of mind; that which does not operate strictly in terms of its own use, but has developed into a standalone feature. Logic originates not from the law of identity, but from the consequences of quantities. Duality is only the most basic geometry.