I want to be able to express set notations fluently in math fields used in machine learning, so I started reading Naive Set Theory by Halmos.
But I have been facing a lot of problems like :
- On pages 1-6 , I encountered
if and only ifand had to go to Wikipedia, to actually understand it .
- Also , I had to search Math.SE to understand such sentences as :
It is equally harmless if the letter used has already been used with "for some" or "for all". Recall that "for some $x \ (x \in A)$" means the same as "for some $y \ (y \in A)$" ; it follows that a judicious change of notation will always avert alphabetic collisions.
" nothing contains everything "
Every page is a conundrum that requires huge amounts of mental gymnastics. I think I'm not ready to read the book, yet.
Can anyone recommend a better introduction to informal set theory than Halmos ?
My Background : I majored in biology and attended calculus, statistics, real analysis, and linear algebra classes in a university. However, I dropped out of all math classes very early to focus on biology. Now, I want to learn math again. The high school didn't teach any theoretical foundation of math at all.