How to compare infinite sets of natural numbers, so that proper subsets are also strictly smaller than their supersets HT Winston Ewert

I knew I could not have been the only one who questioned Cantor's reasoning:
How to compare infinite sets of natural numbers, so that proper subsets are also strictly smaller than their supersets
HT Winston Ewert
I knew I could not have been the only one who questioned Cantor's reasoning:
How to compare infinite sets of natural numbers, so that proper subsets are also strictly smaller than their supersets
Are there really as many rational numbers as natural numbers? You might answer “Yes” but a better answer would be “It depends on the underlying order relation you use for comparing infinite sets”. In my opinion there really is no reason why we should consider Cantors characterization of cardinality as the only possible one and there is also a total order relation for countable sets where proper subsets are also strictly smaller than their supersets. In this article I want to present you one of them.
HT Winston Ewert
8 Comments:
At 3:17 PM, socle said…
Joe,
The hypernatural and hyperreal numbers are certainly very interesting, but of course we have been discussing the natural numbers here (along with the odd rational number).
If you find Cantor's ideas unacceptable, I'm pretty sure you will find the hyperreals to be completely absurd. Are you ok with "infinitely small" positive numbers? For example, numbers x > 0 such that 1/x is infinite?
Can you conceive of two distinct numbers whose difference is infinitely small?
At 3:31 PM, Joe G said…
You have serious issues. I just take issue with one little and seemingly insignificant part of what Cantor said and you assholes go all batshit mental.
Look I have explained my position such that anyione not on an agenda could understand.
At 3:54 PM, socle said…
lol.
I'm actually fine with different notions of cardinality and so forth. I was lucky enough to be a student of the person who coined the term "hyperreal", and the subject came up once or twice, IIRC. I have actually had interesting discussions with folks about using nonstandard analysis for teaching introductory calculus, so I have no problem with it. I'm sure the others feel the same.
Rather, it's the amusing misunderstandings (wtf does relativity have to do with cardinalities of sets, for example?) that keeps drawing us back to your blog.
At 3:58 PM, Joe G said…
I told you what relativity has to do with it.
As I said small minds just cannot grasp new concepts.
At 4:00 PM, Joe G said…
Now run along and dig your infinite number of holes I don't care about the spacing.
At 4:44 PM, Rich Hughes said…
Joe G: Intellectual selfharmer.
At 6:09 PM, Joe G said…
It makes me very happy to know that you think so.
Thank you
At 6:21 PM, Joe G said…
And nothing says that I am correct any more than the ignorant drivel I am getting that is supposed to refute my claims.
So again I thank you, limpy cupcakes.
Post a Comment
<< Home