-  [WT]  [PS]  [Home] [Manage]

Posting mode: Reply
  1.   (reply to 17837)
  2.   Help
  3. (for post and file deletion)
/sci/ - Science, Technology, Engineering, and Mathematics

Join us in IRC!

•This is not /b/ or /halp/. Tech support has its own board.
•If you are not contributing directly to a thread, sage your post.
•Keep the flaming at a minimum.
•Tripcodes⁄Namefags are not only tolerated here, they are encouraged.
•We are here to discuss sci-tech, not pseudoscience. Do not post off-topic.

•♥ Integris

  • Supported file types are: GIF, JPG, PNG, WEBM
  • Maximum file size allowed is 5120 KB.
  • Images greater than 200x200 pixels will be thumbnailed.
  • Currently 742 unique user posts. View catalog

  • Blotter updated: 2018-08-24 Show/Hide Show All

We are in the process of fixing long-standing bugs with the thread reader. This will probably cause more bugs for a short period of time. Buckle up.

Movies & TV 24/7 via Channel7: Web Player, .m3u file. Music via Radio7: Web Player, .m3u file.

WebM is now available sitewide! Please check this thread for more info.

Math is wack. Americium 21/10/11(Mon)19:07 No. 17837 ID: d2a5e8

File 16339720598.jpg - (29.13KB , 540x960 , 82318465_10206866778304869_8225603218482930759_o.jpg )

Just as Cantor's theorem shows there is no set of all sets, there is also no set containing all truths.

Or to put it another way: it's a truth that all truths can't be collected up into a totality.


Anonymous 21/10/12(Tue)17:14 No. 17840 ID: 126958

I feel like it should be possible to construct an axiomatic system of sets where a set of all sets would not lead to a paradox.

Americium 21/10/12(Tue)23:46 No. 17841 ID: d2a5e8

You most certainly can modify set theory to allow a for maximum set of truths, namely predicative set theories.

However, such predicative theories come with their own issues. For instance, the category of sets is no longer a topos (maybe a pretopos), and so we can't define anything much more than first-order logic.

That being said, I personally wouldn't want to work with a theory of sets that doesn't have all possible powersets and/or function sets.

Americium 21/10/13(Wed)00:01 No. 17842 ID: d2a5e8


No wait, I might have misspoken my second part:

That being said, I still stand by my point that I wouldn't want to work in any set theory without a set of functions between any two sets.

Anonymous 21/11/10(Wed)03:56 No. 17896 ID: 586542

I don't buy this argument
consider a finite set {1,2}
then 1 is in {1} {1,2} and not in {2} {null}
and 2 is in {2} {1,2} and not in {1} {null}
The powersets are generated by the elements of the set.
This is like saying that there is no vector space basis of primes (2,0...)x1+(0,3,...)x2+(0,0,5,...)x3+... = v = (2,3,5,7,...)

Americium!Metal3G/gs 21/11/12(Fri)05:07 No. 17899 ID: d2a5e8

Do go on.

[Return] [Entire Thread] [Last 50 posts]

Delete post []
Report post