Is Infinity Magical?
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Infinity must be magical. It is the great magical equalizer.
For example take two sets- set A = {0,1,2,3,...LKN} and set B = {0,2,4,6,...LKN} where LKN = Largest Known Number. The LKN changes and A's cardinality will be 1/2 of that LKN larger than B's cardinality.
1/2 of the LKN is large number. Yet at some point out beyond the LKN there must be a zener diode avalanche region in which ships fall of the edge of the Earth, because somewhere out there, set A's cardinality and set B's cardinality become equal!
Halleluiah and pass the potatoes.
So what is out there, you may ask?- Why its ole infinity. That tricky magical fucker. When numbers get out to infinity they turn to e's (for element) and all e's are equal. So at the LKN it's impossible to form a bijection, ie no way in hell there could be a one-to-one correspondence. But just smoke a fatty, look out into infinity and chant "It's all equal now, dude".
At least now I understand all of the giggles and laughter when I presented my concept.
Infinity must be magical. It is the great magical equalizer.
For example take two sets- set A = {0,1,2,3,...LKN} and set B = {0,2,4,6,...LKN} where LKN = Largest Known Number. The LKN changes and A's cardinality will be 1/2 of that LKN larger than B's cardinality.
1/2 of the LKN is large number. Yet at some point out beyond the LKN there must be a zener diode avalanche region in which ships fall of the edge of the Earth, because somewhere out there, set A's cardinality and set B's cardinality become equal!
Halleluiah and pass the potatoes.
So what is out there, you may ask?- Why its ole infinity. That tricky magical fucker. When numbers get out to infinity they turn to e's (for element) and all e's are equal. So at the LKN it's impossible to form a bijection, ie no way in hell there could be a one-to-one correspondence. But just smoke a fatty, look out into infinity and chant "It's all equal now, dude".
At least now I understand all of the giggles and laughter when I presented my concept.
posted by Joe G @ 11:10 PM
25 Comments:
At 3:04 AM,
Unknown said…
Well, I'm trying to get my head around your method. I've posted some questions on another (older) thread which I'd be pleased if you'd answer.
Basically I'm trying to figure out how you would do arithmetic with your infinities. And whether you think there is a smallest infinity. And what happens if you subtract an element from a set whose size is the smallest infinity does it then become finite?
At 3:04 AM,
Unknown said…
Well, I'm trying to get my head around your method. I've posted some questions on another (older) thread which I'd be pleased if you'd answer.
Basically I'm trying to figure out how you would do arithmetic with your infinities. And whether you think there is a smallest infinity. And what happens if you subtract an element from a set whose size is the smallest infinity does it then become finite?
At 9:53 AM,
Joe G said…
LoL! My method is so simple 4th graders understand it.
And please try to stay on-topic.
Do you think infinity is a magical equalizer?
At 12:09 PM,
Unknown said…
No, i do not think infinity is a magical equalizer.
If your method is so simple then you can explain the rules of adding, subtracting, multiplying and dividing cardinal numbers.
If A = {1, 2, 3, 4 . . . } and C ={2, 4, 6, 8 . . . }
Then what is the cardinality of A minus the cardinality of C? What is the cardinality of C minus the cardinality of A? What is the cardinality of C divided by the cardinality of A?
At 12:20 PM,
Rich Hughes said…
Your method is so stupid a 4th grader came up with it..
At 7:41 PM,
Joe G said…
If your method is so simple then you can explain the rules of adding, subtracting, multiplying and dividing cardinal numbers.
Explain Cantor's rules of doing so with sets that go to infinty.
If A = {1, 2, 3, 4 . . . } and C ={2, 4, 6, 8 . . . }
A would be greater than B. That's it. There aren't any specific numbers because even the LKN keeps moving.
Also all Cantor sez they are equal.
Again please try to stay on-topic. That you are unwilling to do so tells me that you are way out of your depth.
At 8:01 PM,
Joe G said…
Yeah Richie, a 4th grader who is infinitely smarter than you will ever be.
At 8:12 PM,
Rich Hughes said…
And another sign Joe doesn't understand 'infinite'. Epic laughs though, dough-boy. I like these deep, sustained bouts of ignorant hole-digging. Make up your own logic next, or information measure.
At 8:37 PM,
Joe G said…
Great, more cowardly false accusations. And, just to prove that richie is a coward, anotrher total avoidance of the topic.
At 9:21 PM,
Joe G said…
If A = {1, 2, 3, 4 . . . } and C ={2, 4, 6, 8 . . . }
With my methodolgy, if you subtract C from A you will get {1,3,5,7,...}. IOW exactly what you should get.
However if you use Cantor's methodology you get nothing as he sez A and C are equal in size so there can't be anything left after substracting C from A.
Cantor loses, but I am sure you won't see it that way.
My methodology dividing them would give you 2 (A/C) or 1/2 (C/A).
At 2:33 AM,
Unknown said…
"A would be greater than B. That's it. There aren't any specific numbers because even the LKN keeps moving."
Surely there is no LKN because if anyone proposes one you can just add 1 to it to get a bigger one. Or multiply it by 2.
"My methodology dividing them would give you 2 (A/C) or 1/2 (C/A)."
So the cardinalities of A and C are numbers?
What is the cardinality of A times the cardinality of C?
Is there a smallest infinity?
At 9:48 AM,
Joe G said…
So Jerad is also a coward who refuses to address the OP.
Surely there is no LKN because if anyone proposes one you can just add 1 to it to get a bigger one.
Moron- the LKN keeps changing because we can add 1 to it.
And please do the math- the LKN x 2
I will be waiting here for your answer.
At 2:15 PM,
Unknown said…
"Moron- the LKN keeps changing because we can add 1 to it."
So, there is no LKN. Really.
"And please do the math- the LKN x 2"
So, if the LKN keeps changing then LKN times 2 keeps changing. So, there is no answer.
The cardinality of {1, 2, 3, 4 . . . } times the cardinality of {2, 4, 6, . . . } is 2 times the largest known number?
I can see that the cardinality of {1, 2, 3, 4 . . . } PLUS the cardinality of {2, 4, 6, 8 . . . } might be 2 times the largest common number. But I'd think multiplying them together would get you LKN squared. But, it's your system.
At 2:21 PM,
Joe G said…
Why do you refuse to address the OP?
What are you afraid of?
So, there is no LKN. Really.
There is. You just have to be able to keep up, duh.
The cardinality of {1, 2, 3, 4 . . . } times the cardinality of {2, 4, 6, . . . } is 2 times the largest known number?
Nope.
And what do you get with Cantor's system when you multiply the two infinite cardinalities together?
At 3:31 PM,
Unknown said…
" 'So, there is no LKN. Really.'
There is. You just have to be able to keep up, duh."
What is it then?
"And what do you get with Cantor's system when you multiply the two infinite cardinalities together?"
To be honest, I'm not sure. But I'll try and find out. But what does your system give as an answer?
Is there a smallest infinity? You keep not answering that question. Why is that?
At 7:21 PM,
Joe G said…
Umm, Jerad, you can search the internet for the LKN. Or you can ask your old math teacher.
And I don't answer questions that are irrelevant.
At 2:45 AM,
Unknown said…
The LKN does not exist as far as I'm concerned. My old math teacher taught me that. The largest number that can be stored or represented on a given computer does exist but is different for different machines.
You didn't answer the question what is the cardinality of A times the cardinality of C? Cantor would say you get the same size infinity back. Which helps explain why the cardinality of the positive integers is the same as the cardinality of the rational numbers. But not the reals. Or even the transcendentals.
Not answering questions just because you don't think they're relevant might not be a good idea if you want your method to be rigorous and applicable to all cases.
At 9:39 AM,
Joe G said…
The LKN does not exist as far as I'm concerned.
Then you live in denial. Just don't believe that is some sort of argument.
You didn't answer the question what is the cardinality of A times the cardinality of C? Cantor would say you get the same size infinity back.
How do you know? How can that be proven?
Which helps explain why the cardinality of the positive integers is the same as the cardinality of the rational numbers.
How does that make such an explanation?
Not answering questions just because you don't think they're relevant might not be a good idea if you want your method to be rigorous and applicable to all cases.
Your inability to stay on topic proves that you are a know-nothing coward.
At 4:34 PM,
Unknown said…
" 'The LKN does not exist as far as I'm concerned.'
Then you live in denial. Just don't believe that is some sort of argument."
*shrugs*
" 'You didn't answer the question what is the cardinality of A times the cardinality of C? Cantor would say you get the same size infinity back.'
How do you know? How can that be proven?"
Why don't you answer the question? You're good on the attack but not so good on the response.
You took a Set Theory class so you should know the argument.
" 'Which helps explain why the cardinality of the positive integers is the same as the cardinality of the rational numbers.'
How does that make such an explanation?"
You took a Set Theory class so you should know the explanation.
" 'Not answering questions just because you don't think they're relevant might not be a good idea if you want your method to be rigorous and applicable to all cases.'
Your inability to stay on topic proves that you are a know-nothing coward."
I figured we could cut to the chase and ask questions about certain results your method implied. Which seemed fair and more important. Start a new thread if you'd like. I don't mind. I already said I don't think infinity is some magical threshold beyond which everything becomes equal.
At 6:09 PM,
Joe G said…
I already said I don't think infinity is some magical threshold beyond which everything becomes equal.
And yet your posts say otherwise.
As I said if the number of non-negative integers is greater than the number of positive even integers, IN A FINITE SET, then nothing changes even if both sets go to infinity.
And yet you cannot grasp that and say they are equal. IOW you do think infinity is some sort of magical equalizer!
How the fuck can you deny that?
At 12:11 AM,
Unknown said…
" ' already said I don't think infinity is some magical threshold beyond which everything becomes equal.'
And yet your posts say otherwise."
You've just got to get your head around a different kind of cardinality.
"As I said if the number of non-negative integers is greater than the number of positive even integers, IN A FINITE SET, then nothing changes even if both sets go to infinity."
Depends on the sets doesn't it?
S = {1, 2, 3, 4, 5} and T = {2, 4, 6, 8, 10} have the same size.
Now, let them both go to infinity.
"And yet you cannot grasp that and say they are equal. IOW you do think infinity is some sort of magical equalizer!
How the fuck can you deny that?"
Just because things work differently at infinity doesn't make it magic. Different rules but still consisten and coherent.
At the quantum level things don't behave the same as we normal experience them. Yet no one says that's magic. Some things are different in zero gravity than on earth but that's not magic.
Have you ever studied topology? Weird stuff. Moebius strips (a one sided object) and Klein bottles.
At 7:24 AM,
Joe G said…
Numbers don't care about gravity.
But it's all moot, Jerad. Nested hierarchies are different than Cantor's set theory. They don't need it. And what is in their sets is very important.
At 7:28 AM,
Unknown said…
"Numbers don't care about gravity."
Numbers don't care at all.
"But it's all moot, Jerad. Nested hierarchies are different than Cantor's set theory. They don't need it. And what is in their sets is very important."
Don't know why you were arguing about sizes of infinity then.
Nested heirarchies in the 'tree of life' would be finite sets obviously.
At 7:31 AM,
Joe G said…
Don't know why you were arguing about sizes of infinity then.
That's because you are incapable of following along.
Nested heirarchies in the 'tree of life' would be finite sets obviously.
What "tree of life"?
At 9:52 AM,
Unknown said…
" 'Don't know why you were arguing about sizes of infinity then.'
That's because you are incapable of following along."
Well you were arguing about the cardinality of infinite sets for some reason. I was NOT arguing about nested hierarchies.
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