# Set Theory Questions (check if right)

• MHB
• ertagon2
In summary, there is a conversation about checking the accuracy of some set theory questions. One person notes that one part of question 1 is wrong, but everything else looks correct. Another person asks which part specifically is wrong and the first person responds that there may only be finitely many rational numbers between 4 and 6. The second person questions this and suggests considering numbers of the form $4 + \dfrac1n$ for $n=1,\,2,\,3,\,\ldots$. However, they later realize that they were thinking about countable and uncountable sets.
ertagon2
Could someone please check if these are right?
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Re: Set Theory Questions (check if irght)

ertagon2 said:
Could someone please check if these are right?
One part of q.1 is wrong. Everything else looks correct.

Re: Set Theory Questions (check if irght)

Opalg said:
One part of q.1 is wrong. Everything else looks correct.

Which one? Looks alright to me.

Re: Set Theory Questions (check if irght)

ertagon2 said:
Which one? Looks alright to me.
Only finitely many rational numbers between 4 and 6 ? (Doh)

Re: Set Theory Questions (check if irght)

Opalg said:
Only finitely many rational numbers between 4 and 6 ? (Doh)
Isn't there a finite number of rational numbers for 4<x<6 ?

Re: Set Theory Questions (check if irght)

ertagon2 said:
Isn't there a finite number of rational numbers for 4<x<6 ?
What about the numbers $4 + \dfrac1n$, for $n=1,\,2,\,3,\,\ldots$ ?

Re: Set Theory Questions (check if irght)

Opalg said:
What about the numbers $4 + \dfrac1n$, for $n=1,\,2,\,3,\,\ldots$ ?
Oh nvm
I was thinking about countable and uncaountable.

## 1. What is set theory?

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.

## 2. How do you determine if two sets are equal?

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.

## 3. What is the difference between a subset and a proper subset?

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.

## 4. How do you prove that a set is empty?

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.

## 5. What is the cardinality of a 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|.

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