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A "subset" means you can make it out of the pieces in the original set. No matter what set you begin with, you always have the option to choose no pieces at all--that creates the null subset.
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What set is the union of the sets of non negative integers and negative integers?
It is a universal set
Why all sets have at least one element?
That's not true. All sets have zero or more elements. You can have a set with zero elements - the "empty set".
Does the set of all sets contain itself?
Yes.
What are the equivalents sets?
Equivalent sets are sets that have the same cardinality. For finite sets it means that they have the same number of distinct elements.For infinite sets, though, things get a bit complicated. Then it is possible for a set to be equivalent to a proper subset of itself: for example, the set of all integers is equivalent to the set of all even integers. What is required is a one-to-one mapping, f(x) = 2x, from the first set to the second.
What is it when you have all the elements in two or more sets?
The set of elements that are elements of the two (or more) given sets is called the intersection of the sets.
Why is it non set is a subset of all sets?
Because non set establishes the value of "0". Imagine that it is not empty set, but that it is an invisible value that is always located within a set no matter what the values inside brackets are.
Is the union of two convex sets a non-convex set?
the union of two convex sets need not be a convex set.
What set is the union of the sets of non negative integers and negative integers?
It is a universal set
Which set is a subset of every set?
The empty set is a subset of all sets. No other sets have this property.
Does all sets have subsets?
Yes all sets have subsets.Even the null set.
Does a set of all sets contain itself?
There is no such thing as a "set of all sets". To be more precise, the idea of a "set of all sets" leads to contradictions; therefore this term is avoided in set theory. Check the Wikipedia article on "Universal set" for more details.
What is for two sets the set of all elements that are in either set?
That is called the UNION of the two sets.
What for two sets is the set of all elements that are in either set?
The union of a collection of sets is defined as the set of all distinct elements that are in the collection. This includes the specific case where the collection consists of two sets.
What is the GCF that are no other common factors of the number of set?
All non-zero sets of integers have at least one common factor. It's 1.
Give an example of a subset of R that is not a Borel set?
An example is given here: http://en.wikipedia.org/wiki/Non-Borel_set Any set that is easy to think of will be a Borel set, so an example of a non-Borel set will be complicated. Another approach: All Borel sets are Lebesgue measurable. The axiom of choice can be used to give an example of a non-measurable set, and this set will also be a non-Borel set. See http://en.wikipedia.org/wiki/Non-measurable_set = =
Why all sets have at least one element?
That's not true. All sets have zero or more elements. You can have a set with zero elements - the "empty set".
Does the set of all sets contain itself?
Yes.
