Of course it includes infinities, and when was the last time you saw a postgrad exam whose answers didn’t include an argument with the professor?

That’s actually the correct answer. If you don’t get angry and start an argument, you fail.

The biggest number that can be defined in fewer than twenty words.

In fact the answer was a series of definitions of new biggest numbers, and you only defined one, instead of defining it, using it for its value of trees, then using that new term for more trees.

“The largest non-impossible ordinal that is less than the number of infinities there are.”

The set of real numbers between 0 & 1 is larger than any countable infinity.