This isn’t supposed to be a contest of beliefs but a cooperative effort to resolve disagreements. (But then again, this is a forum, so pretty much everything anyone does here is some sort of competition where people try to prove themselves to be the smartest guy in the room.)
Brain damage did not impair my logic, just my memory.
The link you just sent me implies that I’m not allowed to make ANY argument that shows FOR A FACT that infinite and finite behave differently (supposedly (according to you) by my own reasoning).
Your argument about me contradicting myself by having every boy step forward and still all be holding hands is a fantasy of yours! It violates YOUR reasoning! Not what I’ve presented in this thread.
What I’m saying is that it’s true on the surface, but totally false!
Let me give you the example of why I was sent to hell, and then hell beyond hell:
My argument was simple:
If you make suicide and homicide as easy as you could possibly make it (set suicidal and homicidal tension to zero), that whatever survived, would have inherent purpose to live! That’s the solution to ethics!
The argument was flawless!
I was wrong!
The problem on a higher plane of existence with this argument is that you can’t destroy existence, this “flawless” argument only sends people to hell.
Your argument from your mind seems flawless to you, but it is false!
Well it’s not an infinite SUM! 0.333… is a discernible pattern that goes on forever (thus an infinite sequence!)
This is the problem we’ve been having. Your second quote encapsulates this problem! “If infinite sequences are not infinite sequences, then what kind of sequences are they?”
Well… tautologically, an infinite sequence is an infinite sequence! No argument from me there!
They are ALSO finite! In the form of a simple step procedure (a finite algorithm). Every infinite sequence is equal to a finite algorithm; they are equal.
Let me try to explain why (0.333\dotso) is not an infinite sequence.
When we ask “Is (0.333\dotso) an infinite sequence?” what we’re asking is “Does the symbol (0.333\dotso) represent an infinite sequence?”
This means that we’re asking what the symbol (0.333\dotso) represents and NOT what the symbol (0.333\dotso) is in itself.
When we ask “Are numbers sequences?” what we’re asking is “Does the word represent a sequence?”
Since the word “number” does not represent itself, we do not care about the fact that the word “number” is a finite sequence of letters. In other words, the fact that the word “number” is a finite sequence of letters does not mean that what the word “number” represents (= symbolizes = signifies) is a finite sequence of letters (or a sequence at all.)
In the same exact way, the fact that the symbol (0.333\dotso) is a finite sequence of characters does not mean that it represents a finite sequence of characters (or a sequence at all.)
That symbol, on its own, is a sequence consisting of (8) characters. But the symbol itself does not represent a sequence of (8) characters.
(0.333\dotso) is a symbol representing certain number. And it’s not the only symbol that represents that number. There are many other symbols representing the same number. There are finite sequences of characters such as (0.3 + 0.03 + 0.003 + \cdots) as well as infinite sequences of characters that we cannot write down (since they are infinite) but that we can represent using other symbols (e.g. what is represented by the statement “a sequence that starts with (0) followed by (.) and an infinite sequence of (3)'s” is an example of such a symbol.)
Anything can be represented using any kind of symbol. The fact that you can represent a number using an infinite sequence DOES NOT MEAN that that number is an infinite sequence.
You can represent numbers with horses. That does not mean that numbers are horses.