keiths, argues from and like an asshole

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Now keiths sez:

As has been pointed out with much mirth here and elsewhere, the idea of an LKN is silly.

No, that's just an ignorant-based opinion. And anyone can just as easily say that the idea of infinity is silly.

And keiths, your one-to-one correspondence has been shown to be bullshit as the alignment problem crops up. The one-to-one correspondence relies on arbitrary mapping.

OK, so here is what my opponents have to do:

1- Provide a mathematically rigorous definition of infinity

2- Demonstrate infinity exists

If you cannot do that then you whole "argument" is bullshit.

Might as well relabel infinity as Never-Land.

And if Cantor was such a genius, then he must have been correct about the universe being Created. LoL!

But anyway, as I said, we CAN count the elements in an infinite set. We count and count and count- FOREVER. And the set of non-negative integers will always be twice the count as the set of positive even integers (given my last train scenario). And that goes on FOREVER.

Now asshole sez:

Infinity is logically coherent. The LKN isn’t.

That is nothing but your ignorant opinion, keiths. How is infinity logically coherent when no one can demonstrate that it exists?

Then I said- The one-to-one correspondence relies on arbitrary mapping.


keiths' reply:

So does your “method” 

Only an ignorant ass would say that and here is keiths. My alignment is natural- number to number- it is natural in that the number line remains as is.

keiths tries to answer my challenge:

In any case, it’s easy to meet your challenge:

1.Definition: Set A is infinite if every finite subset of A is also a proper subset of A. 

How is that mathematically rigorous?

2. Proof that infinite sets exist:

a. Assume that infinite sets do not exist. By the definition above, that means that every set has at least one finite subset that is not a proper subset.

b. Consider all finite subsets S1, S2, etc. of the set N of natural numbers. Every such subset contains a greatest element Ln (if there were any elements greater than Ln, then one of them would be the greatest element instead of Ln).

c. Ln is a finite natural number. Therefore Ln+1 exists and is also a finite natural number.

d. Ln + 1 is not a member of Sn, but it is a member of N. Therefore every Sn is a proper subset of N, thus contradicting a).

Assuming that infinite sets don’t exist leads to a contradiction. Therefore infinite sets do exist. 

LoL! What is the value of Ln? The point being is it sounds EXACTLY like my LKN, which YOU sed was silly. Also Ln+1= Ln, dumbass.

keiths sez:

And if Newton was such a genius, then he must have been correct about alchemy. LoL! 

He was, dumbass. Just look what happens in stars and supernovae.

But anyway, as I said, we CAN count the elements in an infinite set.

Oh, really?  

Really, see my train example.

We count and count and count- FOREVER.

Sure, you can count forever.   

Exactly! And one set will ALWAYS have more elements than the other-ALWAYS.

 But you never finish, which means you never get an answer.

You don't have to finish and the answer is the cardinality of the set of non-negative integers is greater than the cardinality of the set of all positive even integers.

Yes, every finite set {1,2,3,…,LNET} will have twice the cardinality of the finite set {2,4,6,…,LNET}, and that will be true no matter how large the LNET gets.   

Even if LNET goes to infinity? It looks like keits has finally acknowledged that I am correct.

But you haven’t answered the real question, which is “does the infinite set {1,2,3,…} have twice the cardinality of the infinite set {2,4,6,…}?”

Yes.

The answer to that question, as Cantor showed, is clearly “no”.  

Excepot Cantor didn't "show" any such thing. He couldn't even show that infinity exists.

And BTW assface, I never said, thought nor implied that infinity was a number. Heck it only exists in some people's minds. And that makes it totally useless.