en.wikipedia.org/wiki/Binary_relation
I would write this as:
ball → John (ball is owned by John or John owns the ball)
doll → Mary (dolls is owned by Mary or Mary owns the doll)
car → Venus (car is owned by Venus or Venus owns the car)
cup → (none) (cup is owned by noone or nobody owns the cup)
(none) → Ian (nothing is owned by Ian or Ian owns nothing)
In this case, cup and Ian are unpaired elements, so they are connected to “(none)”, which is the same as “-”, in the above.
Ok, let’s work with what you’re saying and what’s occurring here.
Infinities don’t complete, it’s a process, the moment you “complete” an infinity, it just keeps going.
So what I’d like to point out in your example here is not that one set has more members than the other set, it just takes twice as long!
It never makes sense with infinity to say one set has more members.
We can additionally play language games here:
“Not paired with anything” on a correspondence list to demonstrate larger infinities. It’s a contradiction. If it’s not paired with anything, it can’t be on a correspondence list to begin with. That’s why it’s called a correspondence list.
Can you define what the word “process” means?
Can you show me how a statement such as “An infinite number of apples” describes something that fits such a definition?
Sure. Are you going to claim to have seen an infinite number of apples when you try?
The thing is Magnus, infinity is not an object, infinity is motion itself! It’s a process, not an object!
All of your arguments treat infinity as an object. That’s not what infinity is. The cosmos is infinite. When the cosmos tries to ‘be itself’ (infinite) it can’t do it, this forces the cosmos to have discernible finiteness. It forces objects. That’s part of the reason existence exists.
But you, for some bizarre reason think that you can do what existence can’t do, make the property of existence (infinity) an object!
The Wiki quote you gave me was either taking wildly out of context, or the Wiki author doesn’t understand what cardinality is. There is no such thing as the “number” of elements of an infinite set until we define what the heck we even mean by that! And the way we define the “number” of elements of an infinite set, we define that as its cardinality – a term with a highly specific technical meaning.
When we speak of cardinality as “number”, we are defining number AS the cardinality; not the other way 'round.
I have been away for a few days and reading backwards through this thread I see that I can be of no further use. If my posts were present or absent, the nature of this thread would not change.
Anyway after reading all this I’m at a loss for words. I don’t see where anything I say would help or influence anyone to understand anything better. I’m definitely .999…'d out.
Thanks for the chat all, if I see anything interesting I’ll jump in but I can no longer find any overlap between my reality and this thread’s. Everyone stay safe out there in these crazy times.
You miss the simple fact that the term “the number of elements” is defined with respect to sets and that both finite and infinite sets are sets.
Since the term “the number of elements” is defined with respect to sets, and since both finite and infinite sets are sets, it is also defined with respect to infinite sets.
The statement “The number of elements in an infinite set” is thus ALREADY well defined.
In fact, the only difference between the two kinds of sets is that the number of elements in a finite set is an integer wheareas the number of elements in an infinite set is a number larger than every integer.
The classification of a set as either finite or infinite is based entirely on the number of elements it has. Without knowing how many elements a set has, or worse, without knowing what the term “the number of elements” means with respect to jt, you cannot decide whether it’s finite or infinite.
Magnus, as was explained to you before (not by me), if you remove the first element and everyone at the same time takes one step back or forward there will again be correspondence (unlike finite sets)
I’m going to expand this argument!
Your argument against this, then became not about Just the first item in the set not being removed (because you lost that debate) but about every OTHER item being removed from correspondence.
But!
If every other item used the algorithm of 1 step back, the next item 2 steps back, the next item 3 steps back etc… all at the same time, then even in your “every other” example, every item would still be in correspondence! This cannot happen with finite sets, as was explained earlier, finite sets would still leave people with hands that they could not hold! With infinite sets, everyone is still holding hands
You and me both, bro.
This is why I warned you a while ago that this thread is in fact only about psychology and not reasoning around the actual topic. As such I’m not surprised that even with your input, when you’re so obviously in a position of expertise relative to others here, you end up feeling like your attempts to inform/explain/teach what you know and they don’t are in vain.
This should be such an obvious red flag to those who you won’t be taught that maybe they’re the problem - but this seems to be what internet debate has become - that this never occurs to them.
Give those who don’t know how to debate quick and easy access to information, and they will use this to quickly skim topics and immediately feel like authorities themselves, unable to know any difference between themselves and those who have properly studied these topics and all those leading up to them in genuine depth over the course of years and years.
Everyone’s an expert these days, with no need to humble themselves by learning how to learn from others anymore, and with such opportunity to proudly share what makes them feel so important with so many other people.
Cognitive biases have never had a better chance to thrive.
Wtf believes what wtf was told to believe:
1.) 0.999… = 1
2.) orders of infinity exist
I dislike generalization but specialization is what becomes the trend nowadays.
Its either a ontological pursuit , a pschochologism, or a profession of mathematical analysis, usually lumped together for others to untangle.
How close to specifications can formerly irreduced quantities can be said to equal to the next numerically significant marker?
Marks on paper are vastly different then the ideas represented there, and even A1 suffers from lack of certain demarcations in that regard.
Ideally, it must be admitted that there are limits that absolutely will prohibit any conclusively quantifiable infinite progression, when science entails the opposite: as an integrate of all sets.
That said, the search goes on for the ultimately reduced quantifiable particle, the so called god-particle.
So named appropriately , but that uncertain absolute is totally identical and not merely relatively so, with the idea of ‘God’.
Yet trillions will be spent , in the name of progress, an engine that resembles more a run-away train that can not be stopped.
But the quest can not be given up for different philosophical reasons then say, the proposition that it is merely to stop-gap the force needed to be applied so that once a body is set in motion, an opposite and equal force needs to be applied to stop it.
That is what pure psychology demands to prevent the ultimate collapse of conscious awareness itself.
The investment requires return, other wise even the philosophical implications will be negated.
And no one goes for that.
And I explained why that’s not the case.
It can’t be in one-to-one correspondence because earlier statements say otherwise.
You stubbornly ignore the stated premises.
I will repeat myself one more time, just in case.
We started with the following situation:
Boy1 → Clone1
Boy2 → Clone2
Boy3 → Clone3
etc
We put the two sets in one-to-one correspondence. We paired every boy with exactly one clone and every clone with exactly one boy. This means that every boy is paired (which means there are no unpaired boys) and that every clone is paired (which means there are no unpaired clones.)
Once you remove Clone1 from the set of clones, you get the following situation:
Boy1
Boy2 → Clone2
Boy3 → Clone3
etc
Boy1 is now unpaired because we removed the clone he was paired with. At this point, there is no one-to-one correspondence between the two sets. In order to restore it, there must be a clone in the set of clones that is not paired – an unpaired clone. But there are NO unpaired clones. We STATED it earlier. And f there were unpaired clones, that would mean there was no one-to-one correspondence in the first place. But didn’t we put the two sets in one-to-one correspondence?
A possible way out is to say that by removing Clone1 a new clone is generated. But the problem with this is . . . that’s not what the word “remove” means. To remove a clone does not mean to remove a clone and add a new one.
Another possible way out is to say that there is no need for an unpaired clone to exist. You can just pair Boy1 with one of the paired clones. But the result of that wouldn’t be a one-to-one correspondence. You’d have a clone paired with TWO boys. One-to-one correspondence requires that every clone is paired with EXACTLY ONE boy.
How can you possibly argue against this?
You can’t.
The best you can do is redefine words to avoid admitting a mistake (on the part of mathematicians, that is, since people who post in this thread are merely following what mathematicians are doing.)
For 1 Magnus, I have repeatedly stated that infinity is not an object, but a process… thus, a new clone is always being created!
But that’s not really the point!
Your bizarre idea that if you add one clone by everyone taking a step back or step forward means that one boy must have 2 clones is absurd, in fact, it’s schizophrenia, it’s psychosis.
The fact of the matter is:
Infinity doesn’t act like the finite. You’re still using arguments as if infinity has an end.
For some bizarre reason, you cannot fathom that every argument of yours in this thread has amounted to: “infinity must be finite”
It’s not too complicated to understand that infinity doesn’t end.
So! If you remove 1 member from the beginning, then if every being on the “larger” column takes one step forward, they’ll all be paired again! That’s how infinity works.
And I have repeatedly stated that infinity is not a process.
It’s my word against yours. How are we going to resolve it?
If we say that the number of people in the world is infinite that does not mean that the number of people is increasing with respect to time.
The word “infinite” does not mean “expanding”.
I am not even sure you understood what I said.
Putting that aside, note that by moving clones around you can neither add new clones nor remove existing clones. “To move” is simply “to change position”. Motion is change in position.
Consider the set of natural numbers (N = {1, 2, 3, \dotso}). You are saying the word “infinite” implies continual increase in size. This means the set of natural numbers is continually increasing in size. So at some point (t_1) in time, the set looks like this: ({1, 2, 3, \dotso}). Then, at some subsequent point (t_2) in time, a new number is automatically added to it. Which one? And I guess the set has been increasing since we first came up with it. Since it has been quite a while since we first invented it, it must have acquired a lot of new numbers by now. I didn’t know that. And then there’s the question of the rate at which it is increasing in size.
Well sure, rate means quite a bit!
That’s why I told you it was primarily a TIME problem before…
Look at this again…
1 —> not correspondent
2 —> 2 (correspondent)
3 —> not correspondent
4 —> 4 (correspondent)
Etc…
If the side with half the “numbers” (as you state) moves four times as fast, then the “smaller” set is the one you declare to be the “bigger” set
I think you missed the part where I said that I disagree with your claim that infinity is a process.
You have to prove that the word “infinite” means what you think it means. I am not seeing you doing that here.
Do you believe the contradiction “completed infinity”?
Why don’t you do some explaining on this for a change!
Explain to me why the COMMON mathematical term for infinity is “COMPLETED! infinity”!!!
The other common term is “BOUND! Infinity”
If infinities are bounded, then they are objects and not processes, if they are unbounded, then they are processes and not objects. See?
Read message above!
Sorry for chain posting. I think mathematicians are not only arrogant, but blatantly contradicting themselves to declare infinities as bounded…
Almost out of fear or lack of self esteem, they need to believe infinity is an object to be controlled. They don’t even care about the DEFINITION of infinity, just though, to feel more powerful in their lives that they feel is insignificant