I put that in that language because that is what a mathematician told me i was trying to explain using common language. I can only go on what mathematicians tell me in terms of language here, but let me explain in common language, because obviously my point was missed.
When talking about numbers, mathematics is the only common language. There are different degrees of complexity (I, for example, do not know thing one about advanced calculus), but even basic addition is considered part of mathematics, and follows the same set of rules.
How numbers are used commonly, not in mathematics, but commonly, as in adding, dividing, and multiplying, using only what is available one a linear number line.
That linear number line includes all real values, including non-integers. It also include negative numbers, which you've handily ignored here.
How numbers are used commonly still follows the rules of mathematics.
0 has it's own unique distinction from numbers o,1, through infinity.
"0" as a value is, by definition, unique, yes.
I won't be an ass and call you for putting down "o" instead of "0". I'll just assume it was a typo.
1 has it's own unique distinction clearly since all numbers after 1 are simply combinations of 1 or can be reducible to a set of '1's.
"1" as a value is again, by definition, unique.
But your claim that everything after can be broken down into a set of 1's is where your claim loses meaning. Everything after zero can be broken down into (insert abritrary positive number)'s. So what?
If I claim that everything after zero can be broken down into 0.1245482's, does that make 0.1245482 the base of all numbers?
Even if you want to go so far as to claiming it has to be something that breaks numbers down into attractive non-decimals, what about 0.5? Even 1 can be broken down into 2 0.5's.
You have ignored the infinite number of positive real numbers between 0 and 1.
2 through infinite are simply a combination of '1'. We dont write out 1, 1, 1, 1 for 4, we write out 4. 4 represents 4 actual distinctions, yet it is shorthand, 1 symboloic distinction for 1,1,1,1. It is false relative to the true of 1. all numbers after 1 are 'symbols' that relate to a set of '1's.
Utterly abitrary. Again, I can pick any non-zero integer. 4 is 8 "distinctions" if I choose to use 0.5. 1 is two distinctions using 0.5, as well.
Perhaps when explaining mathematics to a child it is useful to explain things in terms of positive whole numbers, but the level of abstraction quickly snowballs from that. Even in applied mathematics, you can't simply ignore decimals and negative numbers and expect to do anything useful.
"It is false relative to the true of 1" is mathematically meaningless in the context you've given. 1 represents "true" only when dealing with boolean concepts. Since you're talking about the real number line (for some reason), 1 is no more "true" or fundamental than 0.4, or 0.5, or 6.
Better yet, why not focus on prime numbers as the basis for everything? At least that would have some defined structure to it.
0,1, and 2 carry those distinctions in counting and ordering perfectly. those are the three environments of number used naturally, often without consideration that those distinctions are operating in our minds to make these distinctions.
so in this light, on a linear line, numbers 0 through infinity, 0 is mystery, all numbers come from 0, yet 0 does not exist, 1 is the only 'true' number distinction, and '2' is the first 'false' distinction or combination of '1's on the number line.
No, 0 has a defined value, so does 1. So does 2. 2 is a not a "'false' distinction" of anything. 1 is only "true" in context of certain logic systems. Speaking of which, there are ternary logic systems that use values other than than 0 for unknown (they usually use a symbol), and values other than 1 for true.
On the real number line, 0 is 0, not "mystery".
Mind explaining in more detail what you mean by "all numbers from from 0"? And yes, 0 does exist.
All numbers are infinite. one a infinite number line, there are an infinite number of '3's as well as '1's, there is no difference.
What the heck does this mean? Do you mean to imply that the recurrence of the digits means there are an infinte number of that value?
Sorry, but if that's what you're saying, you're comitting the mathematical equivalent of equivocation. There may be an infinite occurrence of the digit 1, but the value of 1 occurs only once. Same for all other defined values.
Those digits don't carry inherent meaning without being placed in the context of actual values. There may be an infinite occurrence of the digit "4", but the value of 4 appears once, and only once, on the real number line.
And? I know about ternary counting systems, what am I supposed to draw from this? It doesn't even relate to your system of ternary logic.
Hope this clears that up, are you going to respond to our last exchange? I raised some rebuttals to your argument and look forward to reading your responses.
I think my views on things are pretty clear, and I think the other posters did a good job expressing how I feel about this in general in my weekend absence.
I'd like to continue to discuss your views on mathematics and logic systems. It's a nice, non-ambiguous area of discussion that I am familiar with, and it seems to relate at least
peripherally to your ternary logic.
mystery is the conceptual signifier for 0 as is used in ordering and counting
It was a stupid computer joke. If I have to explain it, it won't be funny anymore.
The ternary logic paper that I linked to, it's uses 0,1, and 2, and it applies that logic to propositions that are not reducible into boolean, at least according to the paper. The ternary logic paper that i linked to is not a schematic for electronics.
I'm sure you could make any set of distinctions used in math regarding number, but the distinctions of 0,1, and 2 recapitulate outside of mathematics into semantics, logic, and conceptual framing, whilst the other set of distinctions are soley used and neccesary in math and math alone.
I said "computation", not "electronics". There are distinct connections between computational systems and formal logic, because computers require mathematical logic to do anything. Formal logic systems are often used to help solve computational problems.
0, 1, and 2 are not the only values useful outside of mathematics, and other distinctions are not solely useful inside "math and math alone". See the previous comments about your claims of 1 being special somehow.
Basically, digits like 1 are only special if you want things nice and neat, or if you want to multiply or divide by something without actually doing anything useful.
All the cool kids are into infinte decimals and imaginary numbers now anyway. Get with the program.