Well of course I do not suggest that addition, multiplication, and division is separate outside of the body of greater mathematics, I hope that’s not what you think I am suggesting here.
I am saying that dividing, adding, and multiplying are the most common usage for numbers amongst all of us, it’s basic to use those distinctions of number to exist. We all add, divide, and multiply all the time, even the uneducated and most deranged individual can still say “I have one foot, and another foot”
No disagreement.
So those simple numbers that we use for those purposes are the beginning foundation of mathematics, I‘m sure it’s reasonable to assume that would be an epistemological correct statement.
Sure, simple math is the foundation of more complex math, no disagreement there either.
It’s the same distinction with the negative numbers if you stay in that direction. I’m simply referring to continual lineation amongst the numbers, nothing more.
Okay, as long as you're not ignoring everything less than 0.
So, let’s be clear on where we agree. I am saying that our must fundament usage of number as human beings, counting and ordering, is a reference to a continual lineation amongst those numbers, and inside of that lineation, although infinite in principle, can be made into three distinctions which are solely unique to each set.
You're going to have to clarify what you mean here. The number line can be broken down into infinite gradations, but counting and ordering is not done using the infinite numbers between each whole number, generally.
Specifically, counting and ordering are done using only the natural numbers. Those numbers only include 0, and all positive whole real numbers after it.
So if you say "continual lineation" to mean the infinite number of values between each whole number, it's not part of counting and ordering at all. If you simply mean that the number line never ends, then I agree with you.
I go on to say that the ‘third’ number in that direct order takes on an entirely different distinction by default, it has to, right?
If 0 is solely unique, and 1 is solely unique, then 2 is certainly solely unique from 0 and 1.
After that , sure 2 is solely unique as opposed to all other numbers that order from it, but it has a similarity to those numbers that it doesn’t have with 0 and 1, and that from the number ‘2’ or –2 up or down, all of those numbers are composed of more than one unit. So not only does 2 represent false in OS 012, and in the relationship to a symbol that represents two things as opposed to ‘is’ two things, but it also is false we don’t need to be accurate about 2 ‘being’ those infinite number of expressions in definition, it just ‘symbolizes’ it because that’s it’s function, it’s the first ‘symbol’ to define more than one distinction.
Could you please provide a slightly more rigorous definition of "distinction" in this context?
Let me be clear: Are you saying that 2 has a similarity to the subsequent numbers because it, as well as the numbers after, can be divided into a number of 1's greater than 1? If I'm wrong about that, please correct me.
If you're only working with natural numbers, then you could make the argument that it's somehow special, but that isn't really based in any kind of mathematics.
if you’re thinking ‘well could not 3 or 4 or 5 be just as equally false by this definition?’ The answer is yes, but two is used for it’s simple common place elegance, you cant have any of these numbers without them, they signify the whole of all relationships conceptually, the 0, 1, and 2.
Again, I'm not sure what you mean by "they signify the whole of all relationships conceptually". Are you talking about mathematical relationships, or something else?
If you're talking about mathematical relationships, you'll need a lot more than three digits. Even using a base three counting system, there are concepts that cannot be expressed simply using digits. I'm going to need a clearer idea of what you mean by this to answer in depth.
Make sure you distinguish the quality false takes on, while still leaving it’s inherent meaning (not true) in this framework.
I don’t mean ‘base of all numbers’, I mean ‘base of all conceptions’
Got it. Again, clarify what you mean by "base of all conceptions". Are you talking about it being the base of all mathematical concepts, or something else?
The ordering of distinctions continues. 0.12 still holds those same distinctions, we are just analyzing the singular unit and deconstructing further distinctions that follow the same pattern.
What is the "singular unit" you're talking about here.
No I haven’t, it’s just redundant to include them symbolically.
Why would you need to include numbers as symbols? Am I misunderstanding your intent here?
Yet you don’t create a new number set when you do that, you keep using 0, 1, and infinity to express perfectly your results.
I'm not sure what definition of "set" you're using here. In mathematics, a set is simply a collection of values. They don't even have to be unique values.
How do you express decimals using 1? If you're going to stretch this to include usages of the digit one in decimal places, then you're not really using "1" at all.
Infinity is not really used to express results, it is used as something that can be approached but never reached. You can't however, assign "infinity" as the value of a variable and have it be meaningful.
That’s irrelevant to what I am distinguishing in number and truth values.
Sure, when you're talking about truth values it's probably not useful, but you at least appear to be making broader claims about numbers in general.
If that's incorrect, then you'll need to be clearer when you state things.
1 is the ‘true’ number because all numbers after one are simply an expression of some amounts of units. 1 is the conceptual base for all higher numbers.
This argument only holds with natural numbers. You could probably make some argument that all natural numbers are made up of units of 1 and all decimals are made up of fractions of 1, but to go from there to arguing that 1 is the conceptual base for all higher numbers might be a bit of a stretch.
I suppose in some kind of train of though way it is, but when thinking about numbers, I doubt many people will reduce everything back down to one. Conceptually, I would venture that anyone comfortable with numbers is also comfortable enough with abstraction to deal with a unit like "10" or "5" or "1 million" as a conceptual basis.
I think a more accurate way of describing the conceptual basis for numbers would be to address the issue of places on either side of the decimal.
Again, you could make the argument that we would see everything in groups of ones at each place, but that isn't really seeing "1", it's seeing "1000", "10,000", "1,000,000", "0.01", etc.
If that is what you're trying to say, then I don't disagree with your conclusion, I just think you need to state it more clearly.
The ‘basis’ of everything is our perception. That is what I base everything on. Inside of the set ‘perception’, there are three unique distinctions that are also found in what we perceive as number, in the order and counting sense. There is continual recapitulation. I dont know how, or if, recaptiulation is addressed mathematically, if you know please share.
You mean "review and summary", correct?
I suppose you could argue that checking equations is a form of review and summary in mathematics. If you mean something more by this, you'll need to further define it.
Yes, and in truth values, mystery is 0 and not FALSE (2)
Depends on the system you're using. There are systems of true/false that use 0 as false, but it really depends on what you want to do with it. If you want to be able to perform logical calculations, the precise values are important.
In mathematics, 0 is not 2, the distinction of 0 is not the same distinction as 2. or 1.
Define "distinction" in this context, please.
What integer is the center of the number line? It’s obvious –4, -3, -2, -1, 0, 1, 2, 3, 4
No number is the "center" of the number line, if you mean the infinite number line. 0 looks nice because it's between the positive and negative numbers, but it's not technically the center, because there are infinite values. Any given value has infinite numbers before and after it, and hence cannot be the center.
It may or may not be the center of a given finite number line. If I use 1, 2, 3, 4, 5 as my number line, then 3 is the center.
Those numbers just don’t ‘stop’ somewhere, not conceptually. They are continuous. Don’t confuse my argument as saying that this means objective reality is continuous, it may or may not be, that’s another argument, but in counting, conceptually and abstractly, that number line doesn’t stop, it continues.
I didn't think you were arguing that reality was continuous, don't worry.
Sure, the natural number line continues to infinity, if that's the number line you mean.
It is impossible to add the value of the sum total, there is no sum total, so there can be no number that could account for that sum total. Inside of this infinite set, there are an infinite number of 1’s, and an infinite number of possible combinations of 1’s. 2 and 3 become really arbitrary at this point, there is just as many ‘2’s as ‘12’s.
Again, not sure what you're getting at. There are an infinite occurrence of each digit, but that doesn't really mean anything.
Do you see the subjective to the point of view element of 2 yet?
Clarify what this means.
No, it’s just an infinite environment. Infinity is nothing more than a continuation of finites. There are an infinite number of finites, you cant have a sum by default.
True, yes.
You could use a metaphor and say that finite is the noun and infinite is the verb.
I'm not sure how this works as a metaphor for numbers.
Yes, but in principle it could occur as often as it needed to.
Think about it. Infinite finites. How many ‘sets of 4’ can be distinguished in an infinite number line? There is the set of 1-4, the set of 5 – 8, the set of 9-12, etc etc etc ad infinitum.
Oh, you mean sets of 4 values. It appeared from what you wrote that you believed that the value 4 could occur an infinite number of times, which is simply incorrect.
Yes, there are an infinite possible number of sets of 4 values on any given infinite number line, but that in itself doesn't really do or mean anything. Was there a larger issue there or was that just a statement of fact?
If you're just saying that there are an infinite possible number of
n element sets on an infinite number line and nothing more then, sure, you're correct.
Any references I make to ternary logic (specifically the paper I sent using 0, 1, and 2 as truth values in propositions that do not contain Boolean structures), base three counting, or even maybe logic or Taoism simply give you more examples how three values can, and have, significant mathematical reasoning to it’s patterning as well as intuitive adaptation .
No, I agree that three-value systems have a place in mathematics. I don't think Taoism does, but base three and ternary logic have an established place in the world of mathematics.
Base three isn't a very useful system for most people, just like binary isn't, or base 8. All it does is provide another way to express the same values as base 10, but it does it in a way that people aren't comfortable with. Computing has a use for things like binary and base 8, but people generally don't gain much by using it.
Homeboy, if your good enough, I may even hire you at some point! Really, I appreciate this very much, I’m willing to discuss this critically and continually if you are.
Sure, why not.
The paper I sent, didn’t it address propositional problems, however? Can you help me here? That paper, from what my understanding allows, seems to suggest that it is doing things with non Boolean structures, i.e things that cant be done in Boolean, but with 0 =unknown, 1= true, and 2= false.
Boolean logic has a distinct place in the world, but it doesn't work for everything. The ternary logic system appears to attempt to address the issue of uncertainty in a singular logic problem, which Boolean logic ignores, while still allowing set operations using the Boolean logic operations (AND, NOT, OR).
That's why the values are important in ternary logic, it makes working with set operations easier and more logical.
In many ways, it appears to be an extension of Boolean logic.
You claimed one was special the same way I did, we agree about the sole distinction that is allowed to 1 in mathematics.
You mean that I agreed that the value 1 would occur only once? That's fine, every unique value has a sole distinction then, assuming that's what you mean by "distinction."
There can be only one thing in one place at one time, in our basic reality that is, I don’t know if that is true in the QM world, but it’s true here and that is what makes 1 so elegant.
I don't know anything about quantum mechanics, so I won't even get into that realm.
Ahhh, I can’t keep up with the cool kids anymore, I’m trying to keep up with my 1 1/2 year old, and he can't even count!
He'll be solving problems using imaginary numbers before you know it.