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Finite & Infinite Sets Video Lecture | Mathematics (Maths) Class 11 - Commerce

85 videos|243 docs|99 tests

Timeline

00:03 Types of Sets
00:04 Infinite Sets
00:47 Finite Sets
01:09 Examples

FAQs on Finite & Infinite Sets Video Lecture - Mathematics (Maths) Class 11 - Commerce

1. What is the difference between finite and infinite sets?
Ans. Finite sets have a specific and well-defined number of elements, while infinite sets have an unlimited number of elements. In other words, a finite set can be counted, and its elements can be put in a one-to-one correspondence with the counting numbers (1, 2, 3, ...). On the other hand, an infinite set cannot be counted or put in a one-to-one correspondence with the counting numbers.
2. Can a finite set be empty?
Ans. Yes, a finite set can be empty. An empty set, also known as the null set, is a set that contains no elements. It is considered a finite set because it has a definite number of elements, which is zero.
3. Are all sets with an infinite number of elements the same size?
Ans. No, not all sets with an infinite number of elements are the same size. Sets can have different sizes, even if they are infinite. For example, the set of natural numbers (1, 2, 3, ...) and the set of real numbers (including fractions, decimals, and irrational numbers) both have an infinite number of elements, but the latter is considered to be larger in size.
4. Is the set of all prime numbers finite or infinite?
Ans. The set of all prime numbers is infinite. There are an infinite number of prime numbers, and they continue indefinitely without an upper limit. This can be proven using mathematical techniques such as Euclid's proof of the infinitude of prime numbers.
5. Can an infinite set contain a subset that is finite?
Ans. Yes, an infinite set can contain a subset that is finite. The size of a subset does not affect the size of the set it belongs to. For example, the set of all natural numbers (1, 2, 3, ...) is an infinite set, but it contains subsets such as the set {1, 2, 3} which are finite.
85 videos|243 docs|99 tests

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