Practice Exercise: Finite or Infinite Sets

# Practice Exercise: Finite or Infinite Sets | Sets and Functions - JEE PDF Download

State whether each of the following set is finite or infinite:

1. The set of positive integers greater than 100

2. The set of lines which are parallel to the x-axis

3. The set of animals living on the earth

4. {1, 2, 3, . . .}

5. The set of circles passing through the origin (0,0)

Please go through the videos again in case you face any trouble solving the problems.

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--Mahatma Gandhi

The document Practice Exercise: Finite or Infinite Sets | Sets and Functions - JEE is a part of the JEE Course Sets and Functions.
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## Sets and Functions

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## FAQs on Practice Exercise: Finite or Infinite Sets - Sets and Functions - JEE

 1. What is the difference between a finite set and an infinite set?
Ans. A finite set is a set that contains a specific number of elements, which can be counted and is denoted by a finite cardinal number. An infinite set, on the other hand, is a set that contains an uncountable number of elements, and its cardinality is not finite.
 2. How can we determine if a set is finite or infinite?
Ans. To determine if a set is finite or infinite, we can count the number of elements in the set. If the set has a specific number of elements that can be counted, it is a finite set. If the set has an uncountable number of elements, it is an infinite set.
 3. Can a set be both finite and infinite?
Ans. No, a set cannot be both finite and infinite at the same time. A set can only have one cardinality, which determines whether it is finite or infinite. If a set has a specific number of elements, it is finite. If it has an uncountable number of elements, it is infinite.
 4. Are all natural numbers considered as elements of an infinite set?
Ans. Yes, all natural numbers (1, 2, 3, 4, ...) are considered as elements of an infinite set. The set of natural numbers is an example of an infinite set because it has an uncountable number of elements. It continues indefinitely without any specific endpoint.
 5. Can a set have an infinite number of elements and still be countable?
Ans. Yes, a set can have an infinite number of elements and still be countable. Countable infinite sets are those that can be put into a one-to-one correspondence with the set of natural numbers. For example, the set of even numbers (2, 4, 6, ...) is an infinite set but can be counted by pairing each element with a natural number (2 with 1, 4 with 2, 6 with 3, and so on).

## Sets and Functions

39 videos|11 docs

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