0.999=1 (or not)
Orders of infinity exist (or not)
I’m going to resolve both in this post.
9/10+9/100+9/1000… does equal 1 if you add
1/10+(0/10) + 1/100+ (0/100) + 1/1000 etc…
To make the argument that 0.999…=1, you have to argue that addition and non operators are EQUAL!!!
A contradiction! So either addition means something, or all numbers are equal to each other without even using operators.
I’m using (to make this proof) an expanding algorithm, as long as it keeps moving (and carrying), 0.9 + 0.1 always equals 1 and 0.99 + 0.01 always equals 1!
Have you personally EVER seen an infinite sequence that’s not an algorithm? Have you EVER seen a bound infinity all at once?
Nobody ever has nor ever will. Because infinity just keeps going and going and going. By definition!
That means that no matter how far you look, it just keeps going, because the algorithm doesn’t terminate! in the mathematically ideal sense of what infinite expansion or infinitesimals are defined as.
The only POSSIBLE way that your sentence is true is if you’ve seen ALL the members of an infinite sequence in your head!! If you did or do that, then yes, infinity is not an algorithm or process.
That’s quite a claim Magnus … that you hold every number in your head!!!
An algorithm is a finite sequence of instructions on how to perform a task.
A process is what you get when you run, execute or follow an algorithm.
(Note that the two words aren’t synonymous. Not only that but algorithms aren’t even processes.)
An infinite sequence is not an algorithm for two reasons:
because algorithms are FINITE sequences (whereas infinite sequences are INFINITE sequences)
because algorithms are sequences of SPECIFIC THINGS (namely, instructions on how to perform a certain task) (whereas infinite sequences can be sequences of pretty much anything e.g. animals)
It has ABSOLUTELY NOTHING to do with whether one can hold all of the members of an infinite sequence in one’s head or not.
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:
Algorithms cannot (and so they do not) execute anything. (It is computers that can execute things, things such as algorithms.)
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.
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.
The output of an algorithm is the algorithm itself
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.
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.
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.