Question

Using complete sentences, explain what an infinite set is. In your answer give at least two examples of infinite sets

Answer 1

Answer:

Set of integers is countably infinite set

Set of Irrational number

Step-by-step explanation:

A set when it has cardinality less than the cardinality of natural set.Then the set is called finite set.

When the set  is not finite then the set is called infinite set.

Infinite set are of two types:

1.Countably infinite

2.Uncountable

1.Countable infinite set: when the cardinality of set is equal to cardinality of natural set .Then the set is called countably infinite .

Example:Set of integers is countably infinite set.

2.Uncountable : When the set is not countable or not finite then the set is called uncountable.The cardinality of uncountable set is greater than the cardinality of natural set.

Example:Set of Irrational number

Answer 2

A set is said to be a finite set if it is either void set or the process of counting of elements surely comes to an end is called a finite set.

In a finite set the element can be listed if it has a limited i.e. countable by natural number 1, 2, 3, and the process of listing terminates at a certain natural number N.

The number of distinct elements counted in a finite set S is denoted by n(S). The number of elements of a finite set A is called the order or cardinal number of a set A and is symbolically denoted by n(A). Thus, if the set A be that of the English alphabets, then n(A) = 26: For, it contains 26 elements in it. Again if the set A be the vowels of the English alphabets i.e. A = {a, e, i, o, u} then n(A) = 5.