- #1
ertagon2
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Could someone please check if these are right?
View attachment 7908
View attachment 7908
One part of q.1 is wrong. Everything else looks correct.ertagon2 said:
Opalg said:
Only finitely many rational numbers between 4 and 6 ? (Doh)ertagon2 said:
Isn't there a finite number of rational numbers for 4<x<6 ?Opalg said:
What about the numbers $4 + \dfrac1n$, for $n=1,\,2,\,3,\,\ldots$ ?ertagon2 said:
Oh nvmOpalg said:
Set theory is a branch of mathematics that studies the concept of sets, which are collections of objects. It is used to describe and analyze the relationships between different sets and their elements.
Two sets are considered equal if they have the same elements. This means that every element in one set must also be present in the other set, and vice versa.
A subset is a set that contains all the elements of another set, while a proper subset is a subset that does not include all the elements of the original set. In other words, a proper subset is a subset that is smaller than the original set.
A set is considered empty if it does not contain any elements. To prove that a set is empty, you can show that it has no elements by listing all the elements (if the set is finite) or using logical reasoning to show that no elements can be in the set.
The cardinality of a set is the number of elements in the set. It is denoted by the symbol |S| and can be used to compare the sizes of different sets. For example, if a set A has 5 elements and a set B has 3 elements, we can say that |A| > |B|.
