Finite Sets

Definition of Finite Sets

The meaning of the word ‘Finite’ is ‘having a definite limit or fixed size’. Therefore, the Finite Sets may be defined as the sets that have a definite number of elements or a countable number of elements in them.

In other words, a set A is said to be a Finite Set if it has a definite or countable number of elements present in it. Therefore, Finite Sets have a finite number of elements. Also, the Cardinality of a Finite Set is Finite.

Finite Set Examples

Finite Sets

The above figure shows the 3 sets A, B and C. The elements of the three sets are,

  • A = \{1, 2, 3, 4, 5\}
  • B = \{b, c, d, f\}
  • C = \{1, 2, 3, ......., 30\}

All the sets A, B and C in the above examples have a finite number of elements. The set A has 5 elements, the set B has 4 elements and the set C has 30 elements. Therefore, the above sets are Finite Sets.

Practical Examples of Finite Sets

  • Set of all the months in a year.

We are well aware that there are 12 months in a year i.e., January, February, March, April, May, June, July, August, September, October, November and December. Therefore, the set of all the months in a year has a definite number of elements i.e., 12 and hence it is a Finite Set.

  • Set of all the days in a week.

Similarly, there are seven days in a week viz., Sunday, Monday, Tuesday, Wednessday, Thursday, Friday and Saturday. Therefore, the set of all the days in a week has a definite number of elements that is 7 and hence it is a Finite Set.

  • Set of all the planets in our solar system.

The set of all the planets in our Solar System is also Finite Set because the solar system has a Finite number (8) of planets viz., Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.

  • Set of all the elements in the periodic table.

The set of all the elements in the Periodic Table is Finite Set because it has 118 number of elements.

  • Set of all the books for class 10.

Properties of a Finite Set

The properties of a Finite sets are as follows:

  • The Subset of a Finite Set is always a Finite Set.
  • The Superset of a Finite Set may be finite or infinite.
  • The Union of two Finite Sets is always a finite set.

Frequently Asked Questions (FAQ)

A set A is said to be finite if it has a countable number of elements present in the list or finite sets have a finite number of elements.

The main difference between the Finite and Infinite set is that the Finite sets have a definite or countable number of elements, however, the Infinite Sets have an indefinite or uncountable Number of elements.

Also, the Cardinality of a Finite set is definite. However, the Cardinality of an Infinite Set is not defined.

0 is neither finite nor infinite.

The example of some finite sets are:
1. Set of all the natural numbers which are less than 10.
2. Set of all the whole numbers which are less than 10.
3. Set of all the integers which are greater than -5 and less than 5.
4. Set of all the prime numbers less than 50.

None of the above sets is a finite set because, both the sets have infinite number of elements. The set of all the natural numbers starts with 1 and ends in infinity. Similarly, the set of all the positive integers starts with 1 and ends in infinity.

Quiz on Finite Sets

1. Which of the following set is a finite set?
2. Finite sets have..
3. The set of all the months in a year is a..
4. The set of all the planets in our solar system is an...

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