/sci/ - Science & Math » Thread #10835723

135KiB, 500x522, hat-they-what-they-teach-you-at-harvard-business-dont-30404844.png

View Same Google iqdb SauceNAO

Anonymous Thu 25 Jul 15:04:23 2019 No.10835723 View Reply Original Report

Quoted By: >>10836100 >>10836210 >>10836530 >>10836809

How does ZFC set theory bypass Russell's paradox?

Anonymous

Anonymous Thu 25 Jul 2019 18:11:45 No.10836100 Report

Quoted By: >>10836103

>>10835723
you just call the thing of all sets a “category” instead of a set

Anonymous

Anonymous Thu 25 Jul 2019 18:12:47 No.10836103 Report

Quoted By: >>10836194

>>10836100
err wait no a “class” my bad

Anonymous

View Same Google iqdb SauceNAO you_must_change_your_life.jpg, 360KiB, 1080x1350

Anonymous Thu 25 Jul 2019 18:54:58 No.10836187 Report

Quoted By:

By restricting the comprehension scheme (the naive on by "state a property P and I collect all sets with that property into a set Y for you") with one that is restricted to subsets ("state a property P, give me a set X and I collect all sets FROM THAT SET X with that property into a set Y for you").

The above is a bit too restrictive and so another axiom is affed, replacement, that also allows for searching for parameters fulfilling a property and also guarantees that those are sets (you can think of it as "the image of a function that you can define on X also gives set Y")

Anonymous

Anonymous Thu 25 Jul 2019 18:57:01 No.10836194 Report

Quoted By:

>>10836103
Amazing

Anonymous

View Same Google iqdb SauceNAO applbla.jpg, 260KiB, 1280x1792

Anonymous Thu 25 Jul 2019 18:57:45 No.10836195 Report

Quoted By: >>10836210 >>10836809

By restricting the comprehension axiom. The naive one being "State a property P and I collect all sets with that property into a set Y for you".
The restriction is to one that is restricted to subsets. "State a property P, give me a set X and I collect all sets FROM THAT SET X with that property into a set Y for you".

The above is a bit too restrictive and so another axiom is added, the scheme of replacement, that also allows for searching for parameters fulfilling a property and also guarantees that those are sets. You can think of it as "The image of a function that you can define on X also gives set Y"

Anonymous

View Same Google iqdb SauceNAO kacyhyperwave.gif, 2MiB, 400x600

Anonymous Thu 25 Jul 2019 19:03:30 No.10836210 Report

Quoted By:

>>10836195
>>10835723
Come to think of it, it actually relates to the joke in your image. Of course those books at best claim to contain knowledge about the topic business (a subset X among all topics). It ranges not over all knowledge, but apriori over some subset of it (making that restriction explicit would also ruin most of the joke)

Anonymous

Anonymous Thu 25 Jul 2019 20:55:15 No.10836452 Report

Quoted By:

PS I'm currently cover a bunch of set theory stuff - not at big sets yet, but getting there..

https://youtu.be/SAstOixrpdA

Anonymous

Anonymous Thu 25 Jul 2019 21:27:42 No.10836530 Report

Quoted By:

>>10835723
the nonexistence of { x : x is not a member of x }
is a theorem of ZFC

Anonymous

Anonymous Thu 25 Jul 2019 23:17:26 No.10836809 Report

Quoted By:

>>10835723
It's a two-step program. First, as anon >>10836195 has pointed out, we weaken comprehension. However, if there is a set of all sets, then the restricted and original forms of comprehension are obviously equivalent. So we add regularity on top.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches