Question

Find a positive number smaller than `1/2^1000`. Justify

Answer 1

The given number is `1/2^1000`.

This is a positive number.

As the exponent in the denominator increases, the value of the fraction decreases.

Let’s choose an exponent larger than 1000, for example, 1001

Consider the number `1/2^1000`

We know that `2^1001 = 2^1000 xx 2`

Since 2 > 1, it follows that `2^1001 > 2^1000`

∴ `1/2^1000 < 1/2^1001`

Since `1/2^1001` is a positive number and `1/2^1001 < 1/2^1000`, it satisfies the condition.