Pi is neither an algorithm nor a process. (The word “algorithm” and the word “process” mean two different things. Process is what you get when you execute an algorithm. Algorithms themselves aren’t processes. They are merely descriptions of processes.)
Most importantly, even if Pi is a terminating decimal, it still wouldn’t be a digit.
Well, I already did. Just a couple of posts ago. You even quoted it. Here it is. I made (6) different claims and you have yet to respond to a single one.
I answered every point you made before you made that post.
In short, to all of it, if you believe infinities have beginnings and ends (both), then we have no discussion or conversation.
It’s implied that the endlessness of infinity means that infinity is not an object. It can only be described as a process.
You also completely ignored my point that in infinite sets, if you choose every other number as “non-correspondent” that you can use the simple algorithm of taking 1,2,3 steps forwards or backwards and EVERYONE will still be holding hands again, which is impossible in finite sets.
How about you discuss THAT! Instead of ignoring it for 3 pages!!
I am curious to see if what you’re saying here (that you responded to each one of my points before I raised them) is true.
I didn’t say that “infinities” can have beginnings and ends. I said very clearly that it is infinite sequences that can have beginnings and ends. And I further explained that this is because the word “infinite” simply means “a number larger than every integer”. So when we say that a sequence is infinite, we’re not actually saying that it’s without an end (where by “end” I mean “the last element in the sequence”), but rather, that the number of its elements is larger than every integer. This is exactly the same thing we do with sets. When we say that a set is infinite, we are not saying that it is without an end (because the word “end” is not defined with respect to sets) but that the number of its elements is larger than every integer.
I am pretty sure you did not directly respond to the following point (point #1) anywhere in this thread:
Take any finite set of your choice. You can take the set of ternary digits, for example.
({1, 2, 3})
What does it mean to say that this set has an end?
(You are NOT allowed to answer with “It means the number of its elements is an integer”.)
What’s the last element in this set?
There is no such thing because sets have no order.
How does the word “endless”, which means no more than “without an end”, imply a never-ending process of increase?
I responded to that several times in the past.
The problem with that claim of yours is that it contradicts your earlier statements.
You earlier statements imply there’s no one-to-one correspondence between the two sets.
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.