I once decided that I want to understand real analysis. It's looks exciting, construction of sets of numbers and something else, I forgot already. I learned some logic, propositional logic and predicate logic(the one with quantifiers, functions, relations and etc-etc). But it seems I did something wrong. I still cannot understand that set theory I need to learn in order to understand real analysis. These axioms are too confusing, I mean their symbolic representation. No one really explains how those axioms sound. When I compare axiom in English and axiom in Logical Symbols, I get confused. They do not like even nearly the same. For example, if I try to translate to you "28 ударов ножом", I say "28 stab wounds". It has this meaning. But if you really try look at russian expression you'll be confused, you'll say "Stop there's nothing about wounds and stab wounds...". Yes, it is. If to translate literally to English, it says "28 punches by a knife". Sure it sounds somewhat weird, but it still conveys proper meaning. And what happens when I read some texts on axiomatic set theory, I compare the two expressions that are actually written in different languages(logic and English), I get confused.
They just left expressions without literal translations. But translation is not the main thing, I can do it myself for the most part. The problems is that meanings of literal and proper translations are still seem to be very different. They do not explain why they convey the same meaning. For example I can explain to you why is "28 punches by a knife" is the same as "28 stab wounds".
And another problem is that most of the time they do not say for what variables stand for, like variables y, x, w... They give you an expression and they say what it means in english without actually mentioning what variables correspond to what things(I mean, sets, elements of the sets and so on.)
When these three problems merge together, it nearly impossible to understand anything. It really like trying to understand some asian language with their weird looking symbols.
I need your help. What have I do to learn real analysis? May be I have to continue to learn logic? May be that's why I do not automatically understand what axioms are trying to say? Is that because I am not enough "mathematically tough"? I don't even know mathematical analysis. Or the problem is not only in me, may be it is the texts I read so far aren't so much good?
Where did I might have messed up? Can you tell me how you learned set theory and real analysis? What books or textbooks or anything else were helpful to you? Thank you. Yo will really help me and anyone else who struggles with the same type of problem, if there are such people.