For episodic tasks with an absorbing state, why can't $\gamma=1$ and $T= \infty$?
In Sutton and Barto's book, they say that, for episodic tasks with absorbing states that becomes an infinite sequence, then the return is defined by:
This allows the return to be the same whether the sum is over the first $T$ rewards, where $T$ is the time of termination or over the full infinite sequence, with $T=\infty$ xor $\gamma=1$.
Why can't we have both? I don't see how they can both be set to those parameters. It seems like, if you have an absorbing state, the rewards from terminal onward will just be 0 and not be affected by $\gamma$ or $T$.
Here's the full section of the book on page 57 in the 2nd edition
I think the reasoning behind this also leads to why for policy evaluation where
"Has an existence and uniqueness guarantee only if $\gamma < 1$ or termination is guaranteed under $\pi$"(page 74). This part I'm also a bit confused by, but seems related.