Question

Can we show that$0.01001000100001......$ is an irrational number using the contradiction method?

Answer 1

Any number which cannot be expressed in the form of a simple fraction is termed an irrational number.

The number cannot be expressed as $\frac{\mathrm{p}}{\mathrm{q}}$ where $\mathrm{p}$ and $\mathrm{q}$ are integers and $\mathrm{q}\ne 0$ are known as irrational numbers.

If we try to express an irrational number in the decimal form then it is neither terminating nor recurring.

Examples of $\sqrt{2},\sqrt{3}$the value of$\mathrm{\pi }=3.14159265358979\dots$

In the given number $$\mathrm{0.01001000100001......}$$the decimals are neither terminating nor recurring. Hence it is a contradiction of rational numbers.

Hence, it is an irrational number.