What are some cool topics that seem hard but once you learn them

>>9100719
Senior level university physics student and I still don't know what half of those mean.

In order, me guessing:

>A intersection B, so only where the two sets match up is in the new set. I think that's how to explain that.

>A set

>Uhh, no clue. Looks like a rounted less than or equal to, but for sets haha.

>A isn't in B at all?

>a as a subset of A?

>x isn't a subset of A?

>shit. don't remember

>???

>???

>wtf

>>9100723
>A intersect B
>a set
>A is a subset or is equal to B
>A is not a subset of B
>a is an element of A
>x is not an element of A
>I'm gonna presume this is supposed to be O, the empty set
>biconditional (iff) logical operator
>universal quantifier
>existential quantifier
you oughtta study this stuff, my guy

>>9100723
>Senior level university physics student
Dude what

You're clearly smart so go buy any book on set theory or propositional logic and skim through it and your mind will be blown by how cool the topic is lol it allows you to express very complicated logical concepts and used set based reasoning in a very compact mathematical language. I don't know how you can not know these as a senior level university physics student but:

>A ∩ B
A intersect B i.e. "the set of elements in both A and B"
>{ }
Yeah just a set, in this case an empty one. One like {1, 3, 7} would be a set containing 1, 3, and 7
>A ⊆ B
A⊂B means "A is a subset of B" meaning "every element of A is also in B" and in this case A ⊆ B with the underline means "every element of A is also in B or they also might be equal sets" with the lack of an underline typically meaning a strict subset meaning they can't be equal
>A ⊄ B
A is not a subset of B
>a∈A
a is an element of set A
>x∉A
x is not an element of set A
>O
This copy and pasted wrong, I think it was meant to be the "empty set" symbol O oops
>↔
Typically used as P ↔ Q meaning "proposition P is true if and only if proposition Q is true" or in other worst "if P is true then Q is true, and also if Q is true then P is true"
>∀
This is typically used like ∀ x∈A i.e. "for all elements x in A", then you give a property for instance "for all elements x in A, function f is greater than 2" and then you can use set builder notation to build sets containing this property for instance {b∈B | f(b) > 2} which means "the set of all elements b in set B such that f(b) is greater than 2"
>∃
"There exists" which is used in propositional logic for instance "If there exists an element a in set A such that f(a)>2 then Q" i.e. ∃ a∈A, f(a)>2 → Q

organic chemistry tbqh

In highschool the highest level math I took was precal, which was hard for me to understand at the time because I never practiced or did homework. One day I walked into my friends class to wait for him to get out and it was a calculus class. I was amazed how it mostly seemed like a bunch of random letters and variables everywhere, but after taking calculus 2 in college, it all made perfect sense to me. Crazy how when we're so desperate to learn something, we eventually will learn it no matter what as long as we desire to.

>>9100719
i don't think pic related will ever be easy in any sense to anybody

>>9100743
this.