8 items are filed under this topic.








Some questions about sets 
20191215 

From M.Azzi: Hello,
(I)  In set theory can a given set contain both elements and subsets, as "elements", as in :
A = {1,2,{},3,{{3}},8}
If yes :
1  then, is A = 6 ?
2  if the empty set is a subset of every set,
2. 1. does {} = {{}}, {{{}}} etc? , and if the is true what are the respective cardinals of the latter three? (0,1,1?).
2 . 2. Why isn't {1} equal to {{},1}? and why should these two be equal without having the same cardinality?
Sorry if my questions are not well expressed.
Thank you for the great service you provide. Answered by Harley Weston. 





Combinations of cities 
20191203 

From Oliver: Hi!
I'm looking to find out how many combinations (non repeating) there are for 6 cities.
If we name the cities A to F, possible combinations would include;
A.
A, B.
B.
A, B, C.
A, C.
B, C.
C.
and so on.
Thank you! Answered by Penny Nom. 





A question about the empty set 
20180617 

From Andrey: Hello there!
I got that an empty set is a subset of every set.
There is a question.
Is an empty set an element of every set?
∅ ⊆ {x}True
∅ ∈{x}?
Sorry if the question is easy. A set theory is a bit confusing. Answered by Penny Nom. 





A question in set theory 
20150225 

From Jared: If a set A={1,2,3} and set B={ {}, 1}
Can B be a subset of A? Since every Set contains an {} ? Answered by Robert Dawson and Claude Tardif. 





The empty set 
20080929 

From wahab: Why a null set is called a set?
the definition of set includes that a set is a collection of well defined objects
But a null set is having no value. Answered by Harley Weston. 





The empty set is a subset of every set 
20061114 

From Narayana: The empty set is a subset of every set Answered by Stephen La Rocque and Penny Nom. 





Sets and elements 
20020822 

From Dianne: I want to know why its okay to say that, for example, 6 is an element of the set of integers, but you get counted off for saying that the set of 6 is an element of the set of integers. How come? Answered by Judi McDonald. 





Composition of functions 
20020406 

From Yvonne: In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = x^{2}  4 and g(x) = sqrt(x) The range of f(x), x<=4, is the domain of g(x). BUT, there is no solution in the Real numbers for g(f(x))= sqrt(x^{2}  4). In the solutions it says that this is not a function and therefore does not have a domain or range. Is it a relation? Is it anything? Answered by Claude Tardif. 


