This discussion has VERY little bearing on my points 3 pages ago, and I actually delved into it in a very complex way…
Let’s just chalk all this up to a minor “derail”
Like I explained before…
1/9 (very finite)
Also equals
1/10+1/100+1/1000+1/10000 etc…
In this way, Every finite number equals an infinite number of infinite series, the shorthand of which … is an algorithm (the series is implied from the command)
As far as the topic of the thread is concerned:
Does 0.999… = 1. In the same way that 0.111… =1/9?
(0.111\dotso) is an infinite sequence.
(Disagree.)
(\frac{1}{9}) is a finite sequence.
(Disagree.)
(0.111\dotso = \frac{1}{9}) is true.
(Disagree.)
If #1, #2 and #3 are true, it follows that there is at least one infinite sequence that is a finite sequence.
(I’m inclined to agree with this.)
The problem is that (\frac{1}{9}) and (0.111\dotso) are not sequences. They are numbers. (And it’s also not true that (0.111\dotso = \frac{1}{9}) but that’s a peripheral issue.)
This proves my point that you are not interested in a genuine discussion. Each time you are forced to interact with other people (rather than preach to them) you get uncomfortable.
That’s not a sequence, that’s a sum. You are confusing the two.
(0.111\dots), which is the same as (\frac{1}{10} + \frac{1}{10^2} + \frac{1}{10^3} + \cdots), is an infinite sum. It is not an infinite sequence. There’s a huge difference between the two.
It’s not a finite sequence. It’s not a sequence. It’s a NUMBER.
“It’s a SUM with an infinite number of terms!! That’s what convergence fucking is! A fucking SUM!!
Not a sequence, not a series! It’s a fucking SUM! A SOLUTION to the fucking additive infinite series!
You never addressed the argument that proves infinite and finite behave differently in anything resembling a rational manner.
It is a mathematical FACT that when you remove something (and notice when I pointed out that when you “add” to an infinite set, it’s so absurd that not even YOU are arguing that! ) so the only argument you think you have is removal!
This has been explained to you!
If you remove the first one:
Boy —>
Boy —> clone
Boy —> clone
Etc…
All that NEED fucking occur is that all the boys take ONE step forward, and EVERYONE is holding hands again. This is IMPOSSIBLE!! With finite sets!!
Impossible!!! It’s a fucking PROOF that the infinite works differently than the finite!!
You figured that out. That it disproved you.
So what did you do? You ignored it and then posted this:
Boy
Boy —> clone
Boy
Boy —> clone
Boy
Boy —> clone
Etc…
And I jumped in and said “if you move the first boy up one step and then the bottom two (now) up one step and the (now) bottom three up one step Etc… all at once, everyone will still be holding hands again! But only in infinity is this a FACT!! If this is finite, it’s impossible to do this! Thus: infinite and finite WORK differently!
I did not ignore it. I responded to it by stating that it’s not something that you can do because it is strictly forbidden by your previous claims.
Let’s go back to page 98 where I stated:
Note the bolded part.
In order to restore one-to-one correspondence between the two sets, there must be an unpaired clone to pair with an unpaired boy. But there is no such a clone. All of the clones are already paired. Thus, regardless of how you move your clones, you cannot restore one-to-one correspondence.
You responded to this by saying that the word “infinity” refers to a never-ending process of increase which means that new clones are added continually. So when we remove a clone, a new one is added automatically.
And my response to this was that the word “infinity” does not refer to a never-ending process of increase (that it does not refer to a process at all.)
You’re still doing it! You’re ego is invested in nit-picking and not arguments!!!
There is a difference between ‘converges to’ (which is convergence) and ‘converges towards’ which is not convergence. But!! Even that’s a contradiction because the word convergence IN AND OF ITSELF is defined as the finite conclusion of a sequence or series. Infinite or not.
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.)