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Some questions about sets 2019-12-15
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 2019-12-03
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, B.
A, B, C.
A, C.
B, C.

and so on.
Thank you!

Answered by Penny Nom.
A question about the empty set 2018-06-17
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 2015-02-25
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 2008-09-29
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 2006-11-14
From Narayana:
The empty set is a subset of every set
Answered by Stephen La Rocque and Penny Nom.
Composition of functions 2002-04-06
From Yvonne:
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?

Answered by Claude Tardif.



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