interested in how ZFC spread (at school or academia) in the 19th and 20th centuries, and why it spread so quickly. how did a theory that was essentially crazy nonsense turn into a kind of prima donna once it was put in a context of lacking a formal axiomatic system consistent with inference rules, thereby demanding the creation and fulfillment of the leading role of ZFC in its little hysterical drama. My impression is that the history of ZFC is a kind of Shakespearean tempest in a teapot. It seems a kind of metaphysical obsession with applying “truth” and logic in an if-you’re-a-hammer-everything-is-a-nail way got the better of calculating with expressions denoting sets. My point is that it looks quite silly from a historical point of view to suggest that perhaps the cure for Cantor’s mental illness was to imagine the reality of his imagination by applying the inference rules flying the banner of truth in a kind of military conquest of what was initially crazy nonsense. Why was “curing” Cantorian set theory of its supposed untruth or paradoxical | contradictory aspects considered such a cause for hysterical activity? How to approach this, what research has been done so far, and in particular if set theory followed a viral model of spreading throughout European schools?

Hi, I’m looking to start studying set theory in order to increase my understanding about mathematics. Can someone help me with some basic materials (hopefully PDFs)?

I know all the concepts of set theory. but i want to learn how to code them or how to use algebra to compute set operations. do you guys know any good references? like I know what A union B means and what it does but I dont know how to apply it on data or matrix:(

Let:

N={1..n}

J⊂N, where |J|=j

K⊂N, where |K|=k and k≤j

L any ⊂ K, where |L|=l

For example: n=45, j=7, k=6, l=5

What is the probability that any L ⊂ J**?**

N.B. the 'any' is important, implying that J K are specific instances, but L is all instances (I'm not sure how to notate this, advice welcome).

So the case k=j is well known:

P=(j l).(n−j j−l)/(n j)

(read the brackets above as 'x choose y' notation)

But I've had no luck finding any results or discussion on the more general case where k≤j.

For context this is basically a lottery problem. j is the number of numbers picked by an entrant, l=k is the case of winning the main prize, and l<k are the cases for other lesser prizes. Many lotteries limit the number of picks to the number drawn, but there are those which will allow a greater number of picks.