(1 + 1) is not an algorithm. It is a mathematical expression that has the same meaning as (2). Thus, we say, (1 + 1 = 2). This too is a mathematical expression. What it says is that the expression (1 + 1) and the expression (2) have one and the same meaning.
The following, on the other hand, is an algorithm:
Set (a) to an integer of your choice.
Set (b) to an integer of your choice.
Set (c) to 0.
Add the value of (a) to (c).
Add the value of (b) to (c).
Stand up and loudly proclaim the value of (c).
This algorithm takes two integers as an input, calculates their sum and outputs it.
The above algorithm and the expression (1 + 1) represent two different things.
Anything that uses an operator is an algorithm. Whether finite or infinite.
Besides that:
You have unary code. Unary code uses either spaces (instead of zeroes) or enter buttons (instead of zeroes) or both (a form of trinary) (for the SAME symbol)
Unary is either ‘binary’ or ‘trinary’ at the same time.
What does this mean to this discussion?
I don’t know!
But more to your post ((which was totally (again) off topic))
Anytime an operator is used to represent something else, it’s an algorithm. Algorithm is always defined an an implication:
No algorithm?
1+1=1+1
With an algorithm?
1+1=2
Implication! It means there’s implication!
Again! This is you avoiding content.
THIS argument is you criticizing filler instead of the actual point of this post (which you again, ignored)!!
Alright fine. You put in a very clear way “some meat on those bones”
It’s fine if you and I have to repeat ourselves at times…
1.) “algorithms are finite sequences)
Me: this is tautologically true; if an algorithm is infinite, it never stops to yield an output!!!
2.) “infinite sequences are infinite sequences”
Me: true, but also definitely false.
1/9 = 0.111…
Your word “are” also means “equals” in my case above, a finite expression “is” (are) equals an infinite expression.
3.) “algorithms can only be sequences of instructions”
Me: algorithms are finite instructions that imply the sequence. (Not sequences of instructions (You had it backwards)) Some are finite, some are infinite.
4.) “infinite sequences can be sequences of anything”
Me: umm… this is obviously not true. You’re going to kick yourself here. Sequence:(1,2,3) end sequence! Obviously that’s not infinite. The difference between you and I in this discussion is that I KNOW WHAT YOU MEAN!! So I’m not going to hold it against you!!
Let me take this to a side discussion… I used to HATE song lyrics (they always contradict themselves) and then I realized “but I still know what they mean”. And I don’t hate them as much. You contradicted yourself big time here, but I still know what you MEAN!!
What you meant to say is that “any variable can be used as an infinite placeholder”… that’s what you MEANT! You often don’t afford me the same luxury! (Which is why I get so frustrated with you)
5 and 6 are Simply syllogisms that imply the first 4 are true
An algorithm does not need to halt in order to produce an output.
Consider a computer program that consists of an infinite number of one and the same statement: PRINT “HELLO WORLD”. Such a program will never stop running, and yet, it will write to your console as frequently as possible.
The reason why algorithms are finite sequences is not because an infinite sequence of instructions cannot produce an output (that’s not true) but quite simply due the definition of the word “algorithm”.
How can a statement be both true and false? Isn’t that a logical contradiction?
I have no idea what it means to say that algorithms are finite instructions. In fact, I am not aware of the difference between finite and infinite instructions. Can you clarify?
Wikipedia disagrees with you, though. Algorithms are defined as finite sequences of instructions.
So an infinite sequence cannot consist of certain kinds of things? What kinds of things?
I have no idea what that means.
The reason you get frustrated is because you don’t know how to interact with people (specifically, how to discuss ideas with them.)
They don’t imply the first four are true. Rather, they state if some of the previous statements are true, it follows that infinite sequences aren’t algorithms.
So you agree that algorithms are finite sequences and you also agree that infinite sequences are infinite sequences (but you also disagree, for some reason.)
If you agree with both of these statements then to say that an infinite sequence is an algorithm is to say that an infinite sequence is a finite sequence which is a logical contradiction.
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.)