This place has the highest concentration of crazy people that I’ve seen anywhere.
Take it or leave it.
The completed infinity never expresses the zero at the end, the process of counting the infinity to slow expansion does
Do you see the difference ?
Not all who wander are lost - JRR Tolkien
'Cause that fits my definition of finite. The question is, why don’t you want to categorize it? It’s the strangest thing in the world. You say it’s not infinite yet not finite. But you don’t want to categorize it–like it’s not a third kind of thing. What the frick is going on in your mind???
Of course, not! 
And that’s why (0.\dot9) isn’t limited to a specific n. n goes from 1 to infinity.
You can question it all you want. But that’s not what you were doing. You were trying to demonstrate that coming up with a different rendition of the rule gives you different results. That doesn’t put the rule into doubt (at least not for me), it puts your new rendition into doubt because you got an absurd result.
What’s ruining this discussion for me is that you refuse to help me understand your basic assumption: that what applies to finite sets applies to infinite sets. Everything you have argued so far revolves around that. You bring in arguments that work perfectly fine for finite sets, but then expect me to be convinced that they carry over to infinite sets. When I ask you to justify this move, you refuse (because no one tells you what to do), and instead spend exorbitant amounts of energy trying to convince me of something I already know (like every odd point was removed from the line). You know where the bottleneck is, but you keep barking up the wrong tree. Our disagreement boils down to that. In think infinity works differently than you do. My attempts to show you why have failed. Your attempts… well, your attempts are non-existent. That’s the crux. I don’t think we’re gonna get anywhere if you don’t start shifting your focus onto that crux.
Once again:
Take it or leave it.
You mean this?
How does that fit your definition of finite?
There is no (n > 0) such that (\sum_{i=1}^{n} \frac{9}{10^n} = 1). Since (\infty > 0), it applies to (\infty) as well. No matter how large (n) is, the result is always less than (1).
That’s precisely what I am doing.
Maybe you should consider the fact that no injection is possible between (A = {1, 2, 3}) and (B = {1, 2, 3}).
But obviously, you’d rather wallow in frustration. Because it’s an easy, fashionable, thing to do.
The difference between the two of us is that I have patience (a lot of it) whereas you don’t. You complain too much about other people not listening to you or understanding you.
Do you even know what my definition of finite is? You should, 'cause I said it: anything that isn’t infinite. (0.\dot9) isn’t infinite.
Then it’s just wrong. This is your dogma. You’re unquestioned assumption. The above holds for very every finite value of n, therefore it holds for infinite values of n. Everything you argue springs from this assumption, but it’s got nothing to stand on.
Huh??? Do you even know what injection is?
Since when is frustration “fashionable”?
Now you’re just being weird.
“Ecmandu, you must show me (prove) that you are both looking at a tree and not looking at a tree in order to confirm or deny that you are looking at a tree.”
I don’t know what kind of proof school you went to!
So every number that is not greater than every integer is a finite number?
Infinitesimals are finite numbers?
It holds true for every quantity greater than (0). And since (\infty) is a quantity greater than zero (I hope you agree on that one), it holds true for (\infty) just as well.
You know very well what I’m talking about (or at the very least, you are supposed to know, since all it takes is a little bit of attention.)
There is no injective non-surjective function between the two sets.
Do you know what logic is?
It doesn’t work the way you are explaining it.
I have to see a tree and not see the same tree at the same time in order to prove whether the tree is there or not? That’s not logic, that’s some sort of bizarre psychosis
Yes, boggles the mind doesn’t it?!
Yes.
We never came to an agreement that (\infty) is a quantity.
Even if we did, it brings into question whether we can still say (\sum_{i=1}^{\infty} \frac{9}{10^i} < 1) since the whole reason one would agree that (\sum_{i=1}^{n} \frac{9}{10^i} < 1) for all n > 0 is because this says: if you keep adding 9s after the decimal point but you stop at some number n of 9s, then you will still be below 1. Setting n to (\infty) says something very different. It says: if you keep adding 9s and never stop, then you will get a value that [doesn’t] equal 1. That’s a good reason to question whether it holds for any value of n when we allow (\infty) as a value.
I’m “supposed” to know. That’s rich. Just like I was “supposed” to know that (0.\dot9) is not infinite nor finite. The fact of the matter is, your statement was wrong. There is an injective function between A and B. If there were an injective function between any two sets, it would be A and B. But if you add “non-surjective” then sure. What does that prove?
It is indeed psychosis but your own (: That’s not what I said.
The first part of the disagreements comes down to whether infinite also means indefinite.
If it does, then it is not a quantity but rather something like a condition, of a set or whatever.
In as far as the logic itself goes, unless there is some change of the rules after a definite number of decimals, Magnus’ number will always be less than 1. I have no idea how you guys are using all this code, I cant even quote it.
So: “keep adding 9s after the decimal point but you stop at some number n of 9s, then you will still be below 1” is wrong. The formula doesn’t provide for a “stop at some number”, it rather says to keep going indefinitely.
But, not to keep going indiscriminately. You have to keep going with a specific task which by definition precludes any step from altering the result of the previous step. Which is what would have to happen for 1 to be reached.
That’s exactly what you said. It’s on board record.
You said that if I can’t prove that 0.123…0 is not true AND false, then I can’t disprove it.
Absolutely. It makes no sense.
Well, they actually aren’t.
Do you agree that (\infty) is greater than every integer?
Do you agree that an infinite number of apples is more than zero apples? and more than one apple? and two apples? and three apples? and so on?
In other words, do you agree that (0 < 1 < 2 < 3 < \cdots < \infty)?
If you do, then you have to accept that, since (\sum_{i=1}^{n} \frac{9}{10^i} < 1) for every (n > 0) and since (\infty > 0), that (\sum_{i=1}^{\infty} \frac{9}{10^i} < 1).
How do you calculate the result of an infinite sum that never stops?
Magnus!!! Honestly dude!!!
Infinity is not a number!!
It is not greater than or less than an integer!!!
You are so fucking confused on so many levels
“Keep going indefinitely” in the context of (0.\dot9) is the same as “Stop at infinity”.
No it doesn’t! It means “it is an infinity, that which never ends”.