Even if algorithms are infinite (and not finite) sequences of instructions, they are STILL infinite sequences of instructions and not merely infinite sequences (since infinite sequences can be sequences of pretty much anything whereas algorithms are specifically sequences of instructions.)
There is NO algorithm that is an infinite sequence of instructions!!! ALL algorithms are a finite sequence of instructions that CAN imply an infinite sequence!
That’s why you need to learn how to speak properly.
This sentence right here . . .
. . . is probably not a proper English sentence.
Two things:
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Algorithms cannot (and so they do not) execute anything. (It is computers that can execute things, things such as algorithms.)
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Finite or infinite what?
These algorithms you speak of do not “imply” an infinite sequence. Rather, they produce an infinite sequence as their output. In other words, their output is an infinite sequence. The problem is that the output of an algorithm and the algorithm itself are TWO DIFFERENT THINGS. They aren’t one and the same thing.
Why are you disagreeing with me and then repeating what I stated?
Algorithms IMPLY either a finite or infinite sequence!
That’s what I said!
You are misusing the word “imply”.
The algorithms you speak of do not “imply” infinite sequences. Properly speaking, they produce them as their output.
And while I agree that there are algorithms that produce infinite sequences as their output, I disagree that that is a proof that infinite sequences are algorithms.
Let us consider the following statements:
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The output of an algorithm is the algorithm itself
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Algorithms are processes
Of course, both statements are false, but let us accept them as true and see where they lead us.
I believe that the two statements represent the premises in your argument that infinity is process. So what I’m going to try to show now is that accepting them as true leads to conclusions that contradict some of your previous claims.
There are algorithms that output a binary digit. They output a bit: either (1) or (0). This means that bits are the output of some algorithms.
Given that 1) bits are the output of some algorithms, and 2) the output of an algorithm is the algorithm itself, it follows that bits are the algorithms that produced them. And given that algorithms are processes, it follows that bits are processes just as well.
The conclusion is that BITS ARE PROCESSES.
This isn’t true but that’s not the main thing here.
The main thing here is that it contradicts your earlier claim that bits (being integers) are objects.
You’re strictly talking about non-sentient computers.
To humans!!! Algorithms IMPLY!!!
Not really.
This is getting absurd on your part Magnus !
So…
When I state:
0.999. The algorithm as a closed set 9/10+9/100+9/1000 IMPLIES 0.999! It IMPLIES the OUTPUT!!!
When I state 0.999…
The three dots IMPLY !! A rational number and IMPLIES infinite regress!
Yes and I’m saying you are misusing the word “imply”.
There’s no output production without the implication.
Without implication, what does
1+1 equal?
It equals 1+1. !!
Addition is an implication !
Without the implication 1+1 could NEVER equal 2!!!
Never!
Either way, the output of an algorithm is not the algorithm itself. This is the central issue. And as usual, you are avoiding central issues by focusing on peripheral ones.
No shit! I’ve said that many times already. The algorithm implies the sequence but is not the sequence. This whole nonsense line you brought me through is the only thing periphery to actual points that I made:
The actual point is that all sequences are derived from algorithms, implied from the algorithm, and can only be in time. If infinite sequences are outside of time (not motion itself but rather able to ALL be seen at once) then it contradicts the basic definition of endless and there’s no point to call them infinite.
Thus: infinite sequences are always processes
The fact that something is an output of an algorithm does not mean that it is an algorithm itself.
(It can be but not necessarily.)
Some algorithms output infinite sequences. But that does not mean that infinite sequences are algorithms. It simply does not follow.
(And no, they are not algorithms.)
You might as well say that you are the sex that your parents had when they decided to make you. But we all know that you aren’t. You are merely a product of that sex.
You do not go around telling people that the process of Ecmandu’s father having sex with Ecmandu’s mother “implies” Ecmandu and that Ecmandu is therefore precisely that process: the process of Ecmandu’s father having sex with Ecmandu’s mother.
And here’s you lying about what I said in the post above and STILL being on the periphery of my general and specific point (not responding to it!)…
viewtopic.php?p=2768200#p2768200
There’s probably an algorithm for birth, intent or not, and, again, totally on the periphery.
Project much?
You should have EXPLICITLY denied that the output of an algorithm and the algorithm itself are one and the same thing.
You should have said:
“No, the output of an algorithm is NOT the algorithm itself.”
But you didn’t.
Alright, so that’s not what you think. Still, the problem remains. The fact that something is an output of an algorithm does not mean that it is an algorithm itself. It simply does not logically follow. The fact that (2) is the output of an algorithm that outputs the sum of two integers does not mean that (2) is an algorithm. Do you agree?
The mathematical concept of sequence exists outside of time. (As do most of the mathematical entities.)
When we say that a sequence is endless, which means without an end, what that means is that there is no element within it that has the highest index (the element is otherwise known as “the last element”.)
Maybe because I was posting mine while you were posting yours?
So let’s do the “2 reply” of yours really quick!
2 is not an algorithm… right?
Actually!!! 2 IMPLIES EVERY ALGORITHM THAT EQUALS 2!!!
This is transitive !!
When I look at 1+1 I think of 2, when I look at 2, I think of 1+1!
It’s not accurate to state that a sequence is not the algorithm.
I hate talking about this, it means nothing, to the point that I was actually making!!!
Can ANY being hold infinity in their minds at once?
If they can, it’s not infinity; if they can’t then infinity is a process!!
And what does that mean?
Can you be more specific?
What does it mean to say that someone is holding infinity in their mind?
By the way, you have yet to address this:
(Of course, this isn’t the only thing you have yet to address. The list is quite long but for now I am only asking you to focus on this one.)
You made it clear that you agree that algorithms are finite sequences (and not infinite sequences.) I am happy about that. Given that algorithms are finite sequences, how can you say that infinite sequences are algorithms? By saying that infinite sequences are algorithms, you are saying that infinite sequences are finite sequences. Contradiction #1.
The other problem is that algorithms are sequences of INSTRUCTIONS whereas infinite sequences can be sequences of pretty much anything. So how can you say that sequences that can be sequences of pretty much anything are sequences that can only be sequences of instructions? Contradiction #2.
I am waiting for your response, Godot.