Question

illustrate the following statement with example.a.) between any two whole number there are finite number of whole number but infinite number of rational number​

Answer 1

Answer:

We know that whole numbers are

0, 1, 2, 3, 4, ... n

Let us take two whole numbers; say 2 and 4.

Now, the whole number between 2 and 4 is 3.

So, there are finite number of whole numbers between any two whole numbers.

Now, for rational numbers,

$\frac{2 \times 4}{4} \: \: and \: \: \frac{4 \times 4}{4} \\ \frac{8}{4} \: \: and \: \: \frac{16}{4}$

So, rational numbers between 8/4 and 16/4 are

$\frac{9}{4} \frac{10}{4} \frac{11}{4} ...$

For inserting n number of numbers,

$\frac{2n}{n} and \: \frac{4n}{n}$

Any natural number value satisfies n.

Thus, there are infinitely many rational numbers between two whole numbers.