- #36
Moonrat
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matt grime said:If you are now going to declare the "infinite environment is 2 through infinity and 0" then I don'et know what you're remotely getting at. .
I am getting the funny feeling that I may be overcomplicating this in an attempt to match all of your expertise, so please bear with me a bit...
Let's say all number sets can be divided into two distinctions. Finite sets, and infinite sets. An infinite set, according to how I am defining this in the dialectic, by default, has two distinctions inside of it that cannot be escaped or excluded. I know that there are many different sets of infinite in mathematics, but this is not how I am defining it here, this is about how infinity is or can be 'percieved' naturally. Infinity, by it's nature, is not 1, but '2'.
First, there would be what we would call the 'ding an sich' of infinity, which can find no 'true' expression. the philosophical question to this would be 'What is the thing in and of itself of infinity? what can infinity be deconstructed down into? How can we define that which is continuous?'
In math, I would assume this is the same principle that there is no 'infinite number' as there is no 'total' in an infinity, right?
So what is this number then? what is the number that can define that which has no final or finite value other than 0? For this, I assign 0. 0 has no final value, no finite ( at least in the environment of order and addition as Honestrosewater suggested) just as infinity has no final value. Indeed, all infinity can be said to be is merely the 'collection' of finites, which are defined as 1's.
Now, since we have defined this infinity has having no grand total, or a value equal to 0, next, we define how we arrive at all numbers that are 'finites' inside of this grand collection. The grand collection of 1's is what is referenced as the '2', false. There is no such thing as a singular '2' in this infinite set. If there was, then there would be an infinite number of '2's none the less. So in this set, we can then define all numbers as being infinite. We could say the same thing about 3, 4, 5, etc etc that we do about 2. 2 is just the first pure false number, and we refrence it for false for simplicity sake since two is the first distinction of 1. Here, there is no distinction between the numbers 2 through infinity, they are all false. there is only 1 true number, and that is 1 itself. all other numbers are abstractions of the infinite defining the finite for the sake of order and simplicity.
So when 2 is defined as false and assigned to another description of infinity, we define this in the extreme literal sense. 2 is false. there is no '2'. there is no such thing, there is merely a infinite collection of 1's, and nothing more.
You mentioned that mathematicians don’t care if the math is 'real' in the sense that if it has representation in the real world, it is only concerned with the 'rules' of how it is defined conceptually.
I accept that,however, how I am using 0, 1, and 2 has every bit to do with the real or objective world. It is the translation to how we perceive the objective world, so it must. I see that where I need the most work is to understand how the conceptual rules overlap, if at all, in mathematics or mathematical principles, but these principles are very 'real' as they function all the time.
Why is 1 not in this set?
From the pov of what I am referencing, 1 is the only number in that set in the true sense (of 0, 2 through infinity). Now, of course I am not saying that 0 is not a number, or 2 through infinity are not numbers, I am only saying that '1' is the only number with 'balls' if follow my drift. Every thing else is either mystery (like the ding an sich of infinity) or false (like every expression of the combinations of 1)
Because it is "the finite"? This is a departure from the usual ideas, and almost certainly wouldn't agree with whatever notion of numbers the bloke from Princeton had.
well, he did agree, but again, I explained it different to him...remember this is how we 'perceive' these numbers not just inside of us in the conceptual sense, that mathematicians do, but how 'we' in the collective sense perceive them outside of us, and how they apply outside of us.
I don't see why you need to make a distinction between different symbols for the same object: 3=1+1+1.
Ahh! it is not the same object from this POV. 3 is the one 'conceptual' object for THREE real or true objects in objective reality.
I have three bucks in my pocket. In my head, I make '1' distinction that I have '3'. however, when I take the money out of my pocket, I now have 'three' distinctions of 1 dollar. 1 dollar + 1 dollar + 1 dollar. There is no such thing as a three dollar bill ;-)
THAT is the only thing I am talking about, that, and no other. The basic perception of number that if it did not exist, we could not percieve very much, much less mathematics!
You are reading more into it than I do (what I termed "personifying", such as assigning terms like mysterious to 0).
that is the point, however, of this particular work, to 'humanize' these rational principles and define how we humanize them mathematically.
If however, all this princetonian was doing was explaining to you that there is a initial ordinal, successor finite ordinals, and that the set of finite ordinals is infinite, then I can see what he was getting at.
yes...that is where I am getting at too, thank you...
To see this, hold up two fingers and then two more fingers and you have "1+1=3" by counting the spaces between them. So 0 is only special with respect to your common notion of addition
great, now your going to keep me up all night again counting my fingers...hehe, 1, 1, 1,1, 1...
MR