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Some questions about sets 2019-12-15
M.Azzi pose la question :
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.

Harley Weston lui répond.
Combinations of cities 2019-12-03
Oliver pose la question :
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!

Penny Nom lui répond.
A question about the empty set 2018-06-17
Andrey pose la question :
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.

Penny Nom lui répond.
A question in set theory 2015-02-25
Jared pose la question :
If a set A={1,2,3} and set B={ {}, 1}

Can B be a subset of A? Since every Set contains an {} ?

Robert Dawson and Claude Tardif lui répond.
The empty set 2008-09-29
wahab pose la question :
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.
Harley Weston lui répond.
The empty set is a subset of every set 2006-11-14
Narayana pose la question :
The empty set is a subset of every set
Stephen La Rocque and Penny Nom lui répond.
Sets and elements 2002-08-22
Dianne pose la question :
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?
Judi McDonald lui répond.
Composition of functions 2002-04-06
Yvonne pose la question :
In our new text book, the following question occurs: State the domain and range of g(f(x))given that f(x) = -x2 - 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(-x2 - 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?


Claude Tardif lui répond.
 
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