This is definitely a valid criticism. Everyone once and a while I revisit the topic of notation and I’ve basically come to view my superscript notation not as a replacement but as an alternative that is sometimes better.

In defense of this notation though, I think that the standard notation of going (∀x..) is a big tricky for outsiders to follow because keeping track of x when you haven’t internalized a convention is hard. For example, I now know that in topology u and v are open sets, F and G closed ones, calligraphic letters collections of sets, and so on… But when I started it made it extremely difficult to follow proofs.

In any case, I’ve been working through the back of _Counterexamples In Topology_ in this notation when I have free time to “stress test” it. The results have been somewhat interesting in terms of how I’ve rephrased ideas or created new topology specific notations.

I’ve also experimented in alternative notations for other areas of math… That is sorely due for a post.

]]>Hey Nikolay!

It’s interesting that you dislike the second notation. One contributing factor may be the that the low quality images of equations the LaTeX is translated into make superscripts awkward to read…. Then again, this notation probably isn’t for everyone.

One really nice thing about this notation is that it reduces the number of variables you are working with. Makes things more compact, too.

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