@user76284: functions with the same graph but different codomains are usually not identified (otherwise it makes no sense to talk about functions being onto or bijective). Unfortunately introductions to set theory usually don't say this leading to confusion later on.

Johnson answered [by] striking his foot with mighty force against a large stone, till he rebounded from it -- "I refute it thus."

It's very likely that this would necessarily be almost as creative as a mathematician. Note how difficult it is to train humans to do this task: almost all of them who we successfully train to being able to assess math articles, also reach the epsilon-higher level of being able to generate some.

Isn't this more or less pinch-to-zoom as found on touchscreens? Just for the special case where the starting points of the two fingers are two corners of the viewport.

To try to put in one sentence what Thomas wants, for non-readers of German: just as many programs allow one to zoom in by drawing a rectangle in the current viewport over the part one wants to zoom in on, one should be able to zoom out by drawing a rectangle to show which part of viewport should contain the current image.

@XL_at_China, WorldCat says there are copies of both of those books in the National Library of China; perhaps that is accessible to you?

I personally don't know of a good definition of a parse for a context-sensitive grammar, and it seems you need that if you want to define ambiguity as having multiple parses (is there another way to define ambiguity?). It might be interesting to look at less powerful grammars (e.g. conjunctive grammars) with a clear definition of a parse.

While this is obviously overkill, the general technique is so useful that perhaps students should see this proof -- when cardinality is introduced, it's not immediately obvious just how useful it is. For example, even before saying what a computer program is (but knowing that they are specified by strings), one can deduce that there are uncomputable sets, and similarly non-regular languages, etc. I'd say the general idea is that we often have countably many descriptions (programs, grammars, restrictions to $\mathbf{Q}$) but uncountably many objects, so most objects cannot be described.