I am learning real analysis now but I really dislike the notion of limit, infinity... They seems to generate lots of paradoxes and unreasonable results.
For example, when I am reading the uniform continuous notion, there is an example I find quite annoying to accept: Consider the sequence of function: (check the pictures below, I am new so I don't know how to insert math notations, and they wont allow me to display images) definition of the function reason why its pointwise convergent
see its really feels like a fallacy to say that in one place that for every $x$, you can find a $k$ large enough to do blabla, and in another place to say that for every $k$, you can find a $x$ that is large enough to do the opposite thing.
I know its logically right, but I don't think this is the future of mathematics. There is too many procedures and actions, if an alien is learning our notions of math he may not be satisfied I guess.
Thanks for any help and insightful thoughts.
Real analysis is hard. It took mathematicians centuries to figure out careful correct logical ways to describe things like the difference between continuity and uniform continuity, in order to avoid the things that look like paradoxes to you.
I think this really is both the present and the future of mathematics. If you find it alien even after struggling to understand it then perhaps you should find something else to study that pleases you more.