A calculus problem by Zakir Husain

No matter which number you say, the average of 1 and this number will be a smaller real number. Continue this process indefinitely, and still, you can't say what the answer is!

since infinity and infinitesimally small are concepts not a number, therefore no such number exists

Let there be a real number $\epsilon$ which is just next to $1$

This means that it is the smallest number greater than $1$ . Let another number $\psi$ be : $\psi=\frac{1+\epsilon}{2}$ Now $1<\psi<\epsilon$

$\therefore$ $\psi$ is between $1$ and $\epsilon \Rightarrow \epsilon$ is not just next to $1$

This leads to contradiction

$\therefore$ no such number exists