What does it mean to have a recurrence $T(n) = 2T(n)$

Question

I have a recurrence $T(n) = 2T(n)$ that I must find the time complexity for. Although, I have not yet come across a recurrence that did not reduce the problem space like this. I wonder if anyone can provide clarity or insights.

Answer 1

In the form $T(n)=2T(n)$ it is not a reccurrence, it is an equation true if and only if $T(n)=0$.

A recurrence is in the form $T(n+1)=2T(n)$. In this case every element is twice the previous, thus if we know that $T(0)=T_0$ we can easily find that (can be proved by induction)

$$T(1)=2T_0 \quad T(2)=2T(1)=2^2T_0 \quad ...\quad T(k)=2^kT_0$$