Problem of proof in Box 3.1 (Page 55)

[UePG-21]

Hi Professor,

In part 4, isn't $||x^{\ast} - x_n|| \le \frac{\gamma^{n}}{1-\gamma}||x_1 - x_0||$ indicates a linear convergence?

[MathFoundationRL]

As n goes to infinity, gamma^n converges to zero exponentially fast.

[UePG-21]

Thanks for your quick replay!

But based on my understanding, gamma^n is a power function instead of exponential function of n, since there's even not an "e". Also, this definition may be an endorsement of my statement.

[MathFoundationRL]

Convergence is a basic concept in control theory. I am sure that it is exponential, but people may have different definitions.

[UePG-21]

Got it, thanks a lot! The course and book are really great works!