# Talk:Set Theory

Jorin 16:04, 19 July 2012 (EDT)

Hi Chengying! I like the page and it is organized well. Here are my comments.

• Paragraph 1 of Basic Description: Maybe remove "also" from the sentence "Set theory has also become a distinct branch..."
• At the beginning of P2, maybe have a transition sentence to make it flow better
• I like the description of the Venn diagram!
• Maybe a small paragraph on the development of modern set theory in the History section?
• In the "What is a set" section, i feel like the example with the odd numbers is a little strange because you don't specify the elements have to numbers. x could be an odd function. Maybe change "odd" to "odd number" or something, I don't know. Maybe, make it "prime number" instead of "odd"
• In the Axiom of Comprehension, it should be "satisfies" instead of "satisfy"
• There is the word "Click" just kind of sitting there in the description of the axiom of union, is it a "click here"?
• In the section on the difference between two sets, "In words" seems a little awkward, but I don't know how they could be changed
• In the "Properties" section. Introduce the properties with a full sentence. It seems a little awkward when there are just phrases.
• Maybe you could explain this series of equations a bit more If a=b, then (a,a ) = {{a}, {a, a}} = {{a }, {a}} = { {a} } with something like "using the Axiom of Pair" or something like that, just so the reader knows how you are manipulating these equations.
• For the second example of a function, I think you are missing a x2 somewhere in the definitions of G
• For talking about two functions being equal, maybe f=(A, B, G) and g=(A', B, G). I don't think you need the extra prime.
• Also, you have "f=f if and only if f(x)=g(x)", should it be "f=g if and only if f(x)=g(x)"?
• When talking about an inductive set, the second criterion I think should be "if n is a member of I, then (n + 1) is a member of I". You have a instead of n in the if-clause.
• At the beginning of the "Ordinal Numbers" section, the first sentence should be "One very important usage of the natural numbers is to count." I think you left out the "the" and the "s".
• The first paragraph on ordinal numbers is a bit mind boggling. I know it is really hard to describe, but maybe try to describe it in simpler terms. The word "transfinite" is confusing.

--ALL CHECK. Except the one about extra prime. I think it is needed to indicate that we assume at first those are two different functions.