/sci/ - Science & Math

[eqn]\displaystyle \zeta \left( \sum_{k=1}^{\infty} \frac{9}{10^k} \right) = \zeta(1) = \infty[/eqn] Therefore, [math]\displaystyle 0.999\ldots = 1[/math]

>>8502521
I don't consider myself a pro, but I have a firm grasp of (lower) category theory. The trick I use is to simplify stuff. I pretend categories are groups and functors are homomorphisms, and act upon this simplification. This makes things easier to think about, and then the ideas acquired like this are the ones I recheck in a category theoretical sense by adding the forgotten details, what ever they might be.

Similarly, I borrow ideas from homotopy theory while operating with abelian categories. I just say the categories are spaces and functors are continuous maps, which leads to the idea of natural transformations being homotopies. Then, adding the details dropped by my forgetful thought functor, I recheck my stuff to see if it works in a categorical context. So far this has worked.

I can't say if this works for higher category theory, though. I have barely any experience of that. Nevertheless, I'd say you need not be a genius to do category theory.

I was going to tell you my method, but then I realized it was "chicken" and not "children". Maybe some other time.