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Anonymous Sat 05 Feb 14:41:07 2022 No.14189762 View Reply Original Report

Quoted By:

the diagonal argument is retarded and i'm tired of pretending it's true

Anonymous

Anonymous Mon 07 Feb 2022 04:57:03 No.14196652 Report

Quoted By: >>14196655

>>14196649
you when you've raised it as a counterexample to the diagonal argument.

Anonymous

Anonymous Mon 07 Feb 2022 04:58:04 No.14196655 Report

Quoted By:

>>14196652
The diagonal argument indexes sequences, not elements of sequences.

Anonymous

Anonymous Mon 07 Feb 2022 04:58:46 No.14196658 Report

Quoted By: >>14196663

>>14196645
you've said that the diagonal argument doesn't work for finite sets. that's nonsense and only proves that you have no clue. have you ever seen the proof of cantor's theorem? that's what the diagonal argument is. and it applies to both finite and infinite sets.

Anonymous

Anonymous Mon 07 Feb 2022 05:00:00 No.14196661 Report

Quoted By: >>14196675 >>14196686

>>14196627
>But please feel free to describe a diagonal function that works over an arbitrary list of finite sequences
That's trivial. Let f be a function from 1 to the last index of the list or the length of the longest sequence in the list, whichever is greater, such that when s_x(x) = 1, f(x) = 0 and otherwise f(x) = 1.

Anonymous

Anonymous Mon 07 Feb 2022 05:01:29 No.14196663 Report

Quoted By: >>14196669

>>14196658
No, I've said that the diagonal argument has nothing to do with finite sets, and it doesn't.

Anonymous

Anonymous Mon 07 Feb 2022 05:01:44 No.14196666 Report

Quoted By: >>14196679

>>14196636
11 is a complement of the diagonal, so that list proves nothing.

Anonymous

Anonymous Mon 07 Feb 2022 05:03:23 No.14196669 Report

Quoted By:

>>14196663
where does the diagonal argument fail for finite sets then?

Anonymous

Anonymous Mon 07 Feb 2022 05:04:37 No.14196675 Report

Quoted By: >>14196681 >>14196697

>>14196661
I agree that this function is trivial. It reduces to constructing N by successor in the same way that flipping a coin and adding H or T to a list of coinflips also constructs N. Still this has nothing to do with the diagonal argument.

Anonymous

Anonymous Mon 07 Feb 2022 05:05:52 No.14196679 Report

Quoted By: >>14196685 >>14196686

>>14196666
>11 is a complement of the diagonal
By what function?
>where does the diagonal argument fail for finite sets then?
Here:
1 -> {0}
2 -> {1}

Anonymous

Anonymous Mon 07 Feb 2022 05:06:27 No.14196681 Report

Quoted By: >>14196692

>>14196675
>It reduces to constructing N by successor in the same way that flipping a coin and adding H or T to a list of coinflips also constructs N
This is gibberish.

>Still this has nothing to do with the diagonal argument.
It's exactly what you asked for. You have no argument.

Anonymous

Anonymous Mon 07 Feb 2022 05:06:56 No.14196685 Report

Quoted By: >>14196689

>>14196679
your list doesn't satisfy the premise of the diagonal argument.

Anonymous

Anonymous Mon 07 Feb 2022 05:07:28 No.14196686 Report

Quoted By: >>14196697

>>14196679
>By what function?
See >>14196661

Anonymous

Anonymous Mon 07 Feb 2022 05:08:33 No.14196689 Report

Quoted By: >>14196695

>>14196685
>your list doesn't satisfy the premise of the diagonal argument
Correct, because the diagonal argument acts on infinite lists of infinite lists, not on finite things.

Anonymous

Anonymous Mon 07 Feb 2022 05:09:34 No.14196692 Report

Quoted By: >>14196701

>>14196681
>This is gibberish.
>>14196681

Anonymous

Anonymous Mon 07 Feb 2022 05:10:25 No.14196695 Report

Quoted By: >>14196702

>>14196689
it "acts" on any list as long as the indexing sets for the items and the characters are the same.

Anonymous

Anonymous Mon 07 Feb 2022 05:10:47 No.14196697 Report

Quoted By: >>14196703

>>14196686
I agree, see >>14196675

Anonymous

Anonymous Mon 07 Feb 2022 05:12:10 No.14196701 Report

Quoted By: >>14196711

>>14196692
Another schizo post when you have no response. How predictable.

Let f be a function from 1 to the last index of the list such that when s_x(x) = 1, f(x) = 0 and otherwise f(x) = 1.

This function diagonalizes any list. You lose.

Anonymous

Anonymous Mon 07 Feb 2022 05:12:22 No.14196702 Report

Quoted By: >>14196712

>>14196695
So you're imagining a different argument and saying you're imagination is wrong. Okay.

Anonymous

Anonymous Mon 07 Feb 2022 05:13:12 No.14196703 Report

Quoted By: >>14196715

>>14196697
>I agree
Good, so you agree the diagonalization argument applies to any list. Thanks for recant your original claim.

Anonymous

Anonymous Mon 07 Feb 2022 05:14:32 No.14196711 Report

Quoted By: >>14197352 >>14197372

>>14196701
Cool function. And if you use it on a finite list of finite sets then it reduces to a successor function, just like I predicted it would.

Anonymous

Anonymous Mon 07 Feb 2022 05:14:35 No.14196712 Report

Quoted By: >>14196727

>>14196702
Is the following a diagonal argument? If L is a list indexed by the natural numbers such that every item is a binary string with characters indexed by the natural numbers, then the binary string defined by this condition: the x-th character is the opposite of the x-th character of the x-th string of L, isn't included in L.

Anonymous

Anonymous Mon 07 Feb 2022 05:15:34 No.14196715 Report

Quoted By: >>14197356

>>14196703
> Good
> so you agree
> Thanks for recant

Anonymous

Anonymous Mon 07 Feb 2022 05:19:53 No.14196727 Report

Quoted By: >>14196733

>>14196712
Yes. Again, I've never said a "diagonal" over a list finite sequences doesn't prove the list isn't complete, just that
(1) it's always reducible to a successor function
(2) it has nothing to do with OP and the diagonal argument referenced by OP

Anonymous

Anonymous Mon 07 Feb 2022 05:21:39 No.14196733 Report

Quoted By: >>14196737

>>14196727
>Yes
Good. Is the following a true statement? If L is a list indexed by a set X such that every item is a binary string with characters indexed by X, then the binary string defined by this condition: the x-th character is the opposite of the x-th character of the x-th string of L, isn't included in L.
The only that has changed is that "the natural numbers" was replaced by "a set X"

Anonymous

Anonymous Mon 07 Feb 2022 05:24:26 No.14196737 Report

Quoted By: >>14196739

>>14196733
>with characters indexed by X
You will never be a diagonal argument.

Anonymous

Anonymous Mon 07 Feb 2022 05:24:54 No.14196739 Report

Quoted By: >>14196743

>>14196737
Is it a true statement or not?

Anonymous

Anonymous Mon 07 Feb 2022 05:25:52 No.14196743 Report

Quoted By: >>14196747

>>14196739
That
>with characters indexed by X
will never be a diagonal argument?
Yes

Anonymous

Anonymous Mon 07 Feb 2022 05:26:55 No.14196747 Report

Quoted By: >>14196752

>>14196743
Is the following a true statement? If L is a list indexed by a set X such that every item is a binary string with characters indexed by X, then the binary string defined by this condition: the x-th character is the opposite of the x-th character of the x-th string of L, isn't included in L.

Anonymous

Anonymous Mon 07 Feb 2022 05:29:35 No.14196752 Report

Quoted By: >>14196754

>>14196747
>with characters indexed by X
Are you kidding me? Fucking lol

Anonymous

Anonymous Mon 07 Feb 2022 05:30:08 No.14196754 Report

Quoted By: >>14196767 >>14196773

>>14196752
Yes or no?

Anonymous

Anonymous Mon 07 Feb 2022 05:33:54 No.14196767 Report

Quoted By: >>14196771 >>14196773 >>14196774

>>14196754
Your statement has nothing to do with the diagonal argument.
But feel free to write it up in terms of first order logic and I'll let you know if it has any extraneous value.

Anonymous

Anonymous Mon 07 Feb 2022 05:36:32 No.14196771 Report

Quoted By: >>14196780

>>14196767
>Your statement has nothing to do with the diagonal argument.
Except for the fact that if you put X = N you get (what you consider) the diagonal argument.

Anonymous

Anonymous Mon 07 Feb 2022 05:36:52 No.14196773 Report

Quoted By:

>>14196754
>>14196767
To be clear, it has nothing to do with the "diagonal" argument over a list finite sequences, which is what we've been talking about.

Anonymous

Anonymous Mon 07 Feb 2022 05:37:33 No.14196774 Report

Quoted By: >>14196786

>>14196767
>But feel free to write it up in terms of first order logic and I'll let you know if it has any extraneous value.
that has already been done, it's called the proof of cantor's theorem

Anonymous

Anonymous Mon 07 Feb 2022 05:39:12 No.14196780 Report

Quoted By:

>>14196771
The diagonal argument is a special thing for infinite sequences. It has no meaning over finite sequences because other simpler proofs already exist as reductions.

Anonymous

Anonymous Mon 07 Feb 2022 05:41:41 No.14196786 Report

Quoted By: >>14196795

>>14196774
Tell me what part of Cantor's theorem you think attaches to a "diagonal argument" over a list of finite sequences? If a list is finite then 2^|list| is also finite.

Anonymous

Anonymous Mon 07 Feb 2022 05:45:03 No.14196795 Report

Quoted By: >>14196796

>>14196786
cantor's theorem and it's proof don't distinguish between finite and infinite sets, it's true for both. and the proof is literally the diagonal argument.

Anonymous

Anonymous Mon 07 Feb 2022 05:46:24 No.14196796 Report

Quoted By: >>14196805

>>14196795
No, it's not. You've never read any of Cantor's proofs, have you?

Anonymous

Anonymous Mon 07 Feb 2022 05:48:49 No.14196805 Report

Quoted By: >>14196810 >>14196923

>>14196796
do you understand that a subset of X is the same thing as a function X -> {0,1}? do you understand that a function X -> {0,1} is the same thing as a binary string with digits indexed by X?

Anonymous

Anonymous Mon 07 Feb 2022 05:50:46 No.14196810 Report

Quoted By: >>14196818

>>14196805
>a subset of X is the same thing as a function X -> {0,1}?
Good lord, I've been punked. Okay.

Anonymous

Anonymous Mon 07 Feb 2022 05:53:48 No.14196818 Report

Quoted By: >>14196825

>>14196810
good.

Anonymous

Anonymous Mon 07 Feb 2022 05:55:52 No.14196825 Report

Quoted By:

>>14196818

Anonymous

Anonymous Mon 07 Feb 2022 06:52:23 No.14196923 Report

Quoted By: >>14197058

>>14196805
do you understand that you're saying gibberish?

Anonymous

Anonymous Mon 07 Feb 2022 07:22:27 No.14196978 Report

Quoted By: >>14196983

OP here i'm trans btw if that matters

Anonymous

Anonymous Mon 07 Feb 2022 07:28:05 No.14196983 Report

Quoted By:

>>14196978
Is the gender magnet a finite thing or does it diagonalize?

Anonymous

Anonymous Mon 07 Feb 2022 08:14:43 No.14197058 Report

Quoted By:

>>14196923
What exactly?

Anonymous

Anonymous Mon 07 Feb 2022 10:27:44 No.14197224 Report

Quoted By:

>>14196103
>>14196106
everything that seems true and involves infinity is false, so it can't be used in reality

Anonymous

Anonymous Mon 07 Feb 2022 12:09:29 No.14197352 Report

Quoted By:

>>14196711
>And if you use it on a finite list of finite sets then it reduces to a successor function
How so? You keep saying this without any proof.

Anonymous

Anonymous Mon 07 Feb 2022 12:10:30 No.14197356 Report

Quoted By:

>>14196715
You have no argument. Boring.

Anonymous

Anonymous Mon 07 Feb 2022 12:14:43 No.14197372 Report

Quoted By:

>>14196711
You didn't actually deny that the function diagonalizes any list. So you're now saying you were wrong when you almost all lists cannot be diagonalized? OK. No one cares about your gibberish about successor functions.

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