So, Professor Sipser's bio is unreal, I mean no disrespect to the man, nor do I think I could be half the mathematician he is. My issue is--and maybe this is me just not looking at these questions correctly--that the following sample of questions from his Introduction to the Theory of Computation appear to be ill conceived; and they're from Chapter $0$, which makes me question whether the book is worth continuing to read. Examples:
Exercises 0.2: Formally describe the following sets:
The set containing the string $aba$.
The set containing the empty string.
The set containing nothing at all.
What I'm bothered by for all three of these questions is that they begin with "The" when clearly there are infinitely many sets that contain each. I don't know how to interpret these questions and I've never seen elementary set theory questions that seem so, what I would call, imprecise. Maybe they're posed this way intentionally or maybe I'm being a bit dense. Just looking for some advice on whether the book is worth it because I feel a bit disheartened by these.
Here's another example from the same section:
The set containing the numbers $1, 10,$ and $100$.
I mean there are infinitely many of these. I interpret the word "contains", in set terminology, to mean "is a superset of". But then again, I'm a math novice, so it wouldn't surprise me if I was looking at this from a bad angle.
Thanks for the feedback.
In this context - and essentially everywhere - a phrase like "the set containing ---" means "the set containing exactly ---." So the set containing $1,2,3$ is just $\{1,2,3\}$. The indicator is the word "the" - there are many sets containing $1,2,$ and $3$, but "the set containing $1,2$, and $3$" is understood to refer to the unique set containing exactly $1,2$, and $3$.