Question

between any two natural numbers there exist infinitely many a) natural numbers b) whole numbers c) integers d)real numbers​

Answer 1

There are infinitely many (d) real numbers between any two natural numbers.

There are infinitely many real numbers between any two natural numbers.

This is because the set of real numbers is uncountable and dense. Between any two distinct real numbers, there are infinitely many other real numbers that lie in between them.

For example, between the natural numbers 1 and 2, there are infinite decimal expansions such as 1.1, 1.01, 1.001, and so on.

Similarly, between 2 and 3, there are infinite decimal expansions such as 2.1, 2.01, 2.001, and so on.

Therefore, there are infinitely many real numbers between any two natural numbers.

Let us check the other options:

a)natural numbers: between any two natural numbers we can find a finite number of natural numbers only.

b)Whole numbers: Similar to natural numbers we have only finite whole numbers between any two natural numbers.

c)integers also are finite .

So the fourth option is correct.

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