Infinte Sets of Transformers!
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Finally, I get it- well actually I had already been down that path, but here I am again.
Sets' memebers, also know as elements, are transformers. Sure they have one identity in the set but when comparing two sets the elements can be transformed, oranges can be apples, even numbers can become odd numbers and some can remain even! A 2 becomes a 1. A 4 becomes a 2- fucking TRANSFORMERS!
Cantor was way ahead of his time- more so than anyone could have thought. 19th century transformers. Optimus Prime would be proud.
So with the transformer axiom {2,4,6,8,...} does have the same cardinality as {1,2,3,4,...} because the {2,4,6,8,...} can be transformed into {1,2,3,4,...}. And everyone can see that {1,2,3,4,...} = {1,2,3,4,...}.
So I am down with all of that! Just don't tell me that you are comparing the cardinality of the set of non-negative inetgers to the set of non-negative even integers. That would be a lie.
Finally, I get it- well actually I had already been down that path, but here I am again.
Sets' memebers, also know as elements, are transformers. Sure they have one identity in the set but when comparing two sets the elements can be transformed, oranges can be apples, even numbers can become odd numbers and some can remain even! A 2 becomes a 1. A 4 becomes a 2- fucking TRANSFORMERS!
Cantor was way ahead of his time- more so than anyone could have thought. 19th century transformers. Optimus Prime would be proud.
So with the transformer axiom {2,4,6,8,...} does have the same cardinality as {1,2,3,4,...} because the {2,4,6,8,...} can be transformed into {1,2,3,4,...}. And everyone can see that {1,2,3,4,...} = {1,2,3,4,...}.
So I am down with all of that! Just don't tell me that you are comparing the cardinality of the set of non-negative inetgers to the set of non-negative even integers. That would be a lie.
posted by Joe G @ 3:11 PM
21 Comments:
At 4:47 PM,
Unknown said…
Nice try at humour.
Can you now compare the cardinalities of the positive intergers to {1, ½, ⅓, ¼ . . . . }
They are both inifinite sets. They happen to have number elements but that's not the important point. How big are those two sets? Does JoeMaths have an answer?
At 4:49 PM,
Unknown said…
Nice try at humour.
But, the real question is: can you now compare the cardinality of the positive integers with the set {1, ½, ⅓, ¼ . . . . } They're both infinite sets. They both have numerical elements but that's not the important point. The important point is the size of the sets.
What do you say?
At 7:55 PM,
socle said…
Heh. You should ask KF about the Banach-Tarski "Paradox" (actually a theorem). One version says you can take a solid ball, say 1 mm in diameter, disassemble it into finitely many pieces, and reassemble those pieces, without changing their shapes, into another solid ball 1 parsec in diameter (in R^3 of course). That's a helluva transformation there.
At 9:25 PM,
Joe G said…
You know what I say Jerad:
Given 2 sets, A and B, if A contains all of the members of B AND has members B does not, A's cardinality has to be greater than B's.
And the predicted unsupported and cowardly response of "Joe doesn't understand infinity", is duly noted.
Let the flailing begin...
At 9:26 PM,
Joe G said…
BTW the OP was not an attempt at humor. The OP exposes your position as the joke that it is.
At 9:49 PM,
Joe G said…
So I am down with all of that! Just don't tell me that you are comparing the cardinality of the set of non-negative inetgers to the set of non-negative even integers. That would be a lie.
At 1:11 AM,
Unknown said…
"Given 2 sets, A and B, if A contains all of the members of B AND has members B does not, A's cardinality has to be greater than B's."
What does that have to do with comparing {1, 2, 3, 4 . . . } and {1, ½, ⅓, ¼ . . . . } ? You never seem to get around to answering that question. I guess you can't.
"And the predicted unsupported and cowardly response of "Joe doesn't understand infinity", is duly noted."
Well, it is true!!
"Let the flailing begin…"
Better talk to your wife about that.
At 9:14 AM,
Joe G said…
Jerad,
BTW the OP was not an attempt at humor. The OP exposes your position as the joke that it is.
Nice and cowardly of you to try to change the subject.
At 9:23 AM,
Unknown said…
"BTW the OP was not an attempt at humor. The OP exposes your position as the joke that it is."
Needs work.
"Nice and cowardly of you to try to change the subject."
All part of the service!!
At 9:29 AM,
Joe G said…
Yes, youtr position needs a lot of work.
However you are too much of a coward to do any...
At 1:05 PM,
Unknown said…
"Yes, youtr position needs a lot of work."
har, har
"However you are too much of a coward to do any…"
Well, at least I can handle comparing the cardinalities of {1, 2, 3, 4 . . . } and {1, ½, ⅓, ¼ . . . } whereas you' ve choked on this question so many times I figure you're bright blue in colour now.
At 1:19 PM,
Joe G said…
Jerad,
YOU can't support anty of the shit you spew so shut the fuck up.
YOU are too much of a coward to stay on-topic.
YOU are too stupid to grasp the fact that the set of non-negative integers contains all of the non-negative even integers AND has the positive odd integers left unmatched.
At 1:51 PM,
Unknown said…
"YOU can't support anty of the shit you spew so shut the fuck up."
Not my fault you can't understand the counter arguments.
"YOU are too much of a coward to stay on-topic."
All part of the service.
"YOU are too stupid to grasp the fact that the set of non-negative integers contains all of the non-negative even integers AND has the positive odd integers left unmatched."
And you CANNOT tell me how the cardinalities of {1, 2, 3, 4 . . . } and {1, ½, ⅓, ¼ . . . . } compare. Not only can't you handle that but you are not mature enough to admit that you can't handle it.
JoeMaths, everything we need to know we learned in 4th grade.
Which means you don't get transistors. Or GPS. Or lazers. Happy with that?
At 1:56 PM,
Joe G said…
Jerad,
There aren't any counter arguments. You just repeat the same ole standard claptrap.
YOU are too stupid to grasp the fact that the set of non-negative integers contains all of the non-negative even integers AND has the positive odd integers left unmatched.
Wallow in your stupidity.
And your false accusations just prove that you are a coward.
At 3:41 PM,
Unknown said…
"There aren't any counter arguments. You just repeat the same ole standard claptrap."
None that you can understand at least.
"YOU are too stupid to grasp the fact that the set of non-negative integers contains all of the non-negative even integers AND has the positive odd integers left unmatched."
It's not my fault if you can't grasp another matching scheme.
"Wallow in your stupidity."
I'm good. Have you even bothered to acknowledge the fact that you can't address comparing the cardinalities of {1, 2, 3, 4 . . . } and {1, ½, ⅓, ¼ . . . } ? Not that you care of course. I just thought I'd mention it. Again.
"And your false accusations just prove that you are a coward."
I tell you what, you could really improve your standing if you'd just prove that your methods could handle some cases . . . not hard really. Like: compare the cardinalities of {1, 2, 3, 4 . . . .} and {1, ½, ⅓, ¼ . . . } . Can you do that at least?
And the silence continues.
I tell you what Joe, set up a challenge thread. Where you get to ask questions and we get to ask questions. And lets see who even just bothers to answer challenges. How about that?
So, can you match up? Can you compete? Why not try it and find out?
At 1:43 AM,
Unknown said…
Well, I see you haven't even tried to deal with comparing the cardinalities of {1, 2, 3, 4 . . . } and {1, ½, ⅓, ¼ . . . . }
Hardly unexpected.
At 9:20 AM,
Joe G said…
"YOU are too stupid to grasp the fact that the set of non-negative integers contains all of the non-negative even integers AND has the positive odd integers left unmatched."
It's not my fault if you can't grasp another matching scheme.
It isn't a matching scheme. It is a magical transformer scheme.
It's not my fault that you are too stupid to understand that.
Jerad if I set up a challenge thread you will have to prove that infinity exists outside of our minds. And you cannot do that.
So fuck off moron. Not only that you don't grasp the fact that if one set contains all of the members of the other set AND has members the other set does not, its cardinality has to be greater than that other set.
IOW you are already challenged.
At 9:21 AM,
Joe G said…
Well, I see you haven't even tried to deal with comparing the cardinalities of {1, 2, 3, 4 . . . } and {1, ½, ⅓, ¼ . . . . }
I don't do what you want me to do Jerad.
YOU aren't in any position to ask anything of me.
At 9:48 AM,
Joe G said…
So I am down with all of that! Just don't tell me that you are comparing the cardinality of the set of non-negative inetgers to the set of non-negative even integers. That would be a lie.
Jerad is OK with living a lie...
At 1:57 AM,
Unknown said…
" 'It's not my fault if you can't grasp another matching scheme. '
It isn't a matching scheme. It is a magical transformer scheme."
Such a simple concept, that escapes you.
"Jerad if I set up a challenge thread you will have to prove that infinity exists outside of our minds. And you cannot do that."
What do you think 1 + 2 + 3 + 4 + . . . . comes out to?
"So fuck off moron. Not only that you don't grasp the fact that if one set contains all of the members of the other set AND has members the other set does not, its cardinality has to be greater than that other set."
Because it ain't necessissarily so.
"IOW you are already challenged."
Not really. You haven't asked anything I can't answer. Whether or not you understand the answers or agree with them is another issue.
"I don't do what you want me to do Jerad.
YOU aren't in any position to ask anything of me."
Fine, then I'll just judge you based on what you do address.
At 9:22 AM,
Joe G said…
Jerad if I set up a challenge thread you will have to prove that infinity exists outside of our minds. And you cannot do that.
What do you think 1 + 2 + 3 + 4 + . . . . comes out to?
Go for it, Jerad. I bet your sequence ends when humanity ends.
So fuck off moron. Not only that you don't grasp the fact that if one set contains all of the members of the other set AND has members the other set does not, its cardinality has to be greater than that other set.
Because it ain't necessissarily so.
It cannot be any other way.
BTW the magical transformer technique doesn't escape me. Obvioulsy it escapes you though.
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