Russell's Paradox

一個有關數學裡既一大範疇 Set Theory既迷
Russell's Paradox

"define a set  R = { x : x ∉ x }
So, does R belong to R?
If R belongs to R, then R is not a member of itself, ie. R ∉ R.
If R ∉ R, the R belongs to itself.
In either case, we have a contradiction. "

extracted and modified from "Set Theory, Thomas Jech, and Springer."

ngng，簡單黎講，一個唔係自己既自己，屬唔屬於自己
如果屬於自己，咁姐係自己唔係自己
如果唔屬於自己，咁姐係自己係自己
兩者都有邏輯謬誤，所以呢個「唔係自己既自己」，係冇意思既文字
呢種"intuitive notation of set"，叫做
Axiom Schema of Comprehension，不過名唔係咁重要

係Pure Mathematics 2007年Paper 1既Marking Scheme
出左個咁既答案：

形式係同 Russell's Paradox 相似
不過唔知眾AL考生，被AL強姦時有冇諗過呢D野