Set Theory - Tumblr Posts
STE(A)M Meeting
Engineer: What if we added Art to STEM, so it says STEAM? Like a STEAM ENGINE?
Biologist: but i like stems…
Physicist: Sorry, but STEAM’s got my vote. I approve of all 7(ish?) phases of water. I think.
Computer Scientist: I vote for STEAM too, #PC gaming master race
Set Theorist: I will also vote in favor of increasingly large collections of seemingly unrelated things.
Education Professor: That's all very... dumb. F-. But, I have a pretty good idea on how to use the A so I'll vote for it too!
Biologist: :(
Artist: wtf, why am I here? What kinda nerdy sausage party is this?
Education Professor: (on hands and knees) PLEASE PLEASE PLEASE MAKE OUR CURRICULUMS LESS BORING I DON'T KNOW HOW TO STOP ALL MY STUDENTS FALLING ASLEEP IF THEY CAN'T BE CREATIVE PLEASE
[Image description:
A photo of two men leaning against a fence at a building site, with text: ‘tag two blokes who do fuck all’. The men are labelled ‘plus 0′ and ‘times 1′.
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what is your favorite field of math?
How can you have just one! I'll list a few, in no particular order ^^
Abstract algebra
topology
logic
number theory
probability
Set Theory
The reason for most of these is because of Computer Science
@rainbowpopeworld ah yes the glasses being a joke about unpredictability makes sense, thanks! For the purposes of the paradox, I shall set that excellent explanation aside and assume that the only joke about the glasses was that there was no joke about the glasses. Here we go!
Russell's Paradox, glasses joke version:
1) I expected there to be a joke about the glasses
2) I saw no joke about the glasses
3) I considered the very lack of a joke to itself be a joke
4) Thus I do see a joke about the glasses
5) So now (2) is false. Which means that we can't say (3), which means (4) is false. But that means (2) is true again! Oh no!!
In short, there is a joke about the glasses if and only if there isn't a joke about the glasses. A paradox.*
Russell's Paradox, general version:
Define a "set" as a (possibly empty) collection of stuff. Also, sets are stuff.**
Define A as the set of all sets that do not contain themselves.
Does A contain A?
1) If A is in A, then A contains itself, so A is not in A.
2) If A is not in A, then A does not contain itself, so A is in A.
So A is in A if and only if A is not in A.
We broke math.
We fixed math by saying "sets are not allowed to contain themselves."
Which to me feels unsatisfying, but maybe there's more to it that I have yet to learn.
(Also, I've been trying to figure out how to define A such that the general version becomes the glasses joke version. Haven't found an entirely convincing one yet, so it's possible that the glasses joke paradox isn't exactly Russell's Paradox but has a similar vibe.)
*This is resolvable by changing the wording to "I expected him to refer to his glasses, but then he didn't, and thus he made a joke without actually referring to his glasses." So then (2) becomes "I saw no reference to glasses" and (4) is "I saw a joke about glasses" and there's no contradiction. But that's less fun.
**Indeed all stuff is sets, and can all be built from the empty set {}. Or at least that's one way of looking at math.
Michael Sheen: “full of edgy danger” 😇
No... Don't do this to me, please
countability
I have the axiom of choice sitting in a drawer somewhere but i don’t know which :( maybe if I go through each drawer one by one….
it’s a common misconception that maths is all theoretical; they actually keep the 0 in a vault in France and u can go look at it if u got connections.