its super common to open a math, computer science, or physics textbook and have mathematical symbols thrown at you that you never even learned how to read. here's a list of logical symbols that can help you improve your math comprehension!
symbol: A ⇒ B
meaning: “If A, then B.” In other words, “A implies B.” In other words, “If A is true, then B is true.”
example: x = 2 ⇒ x + 3 = 5
symbol: A ⇔ B
meaning: “A if and only if B.” In other words, “If A is true, then B is true. If A is false then B is false.”
example: x = 2 ⇔ x + 3 = 5
symbol: ∵
meaning: “Because”
example: x + 3 = 5 ∵ x = 2
symbol: ∴
meaning: “Therefore”
example: x = 2 ∴ x + 3 = 5
symbol: ∀
meaning: “For all”/“For every”
example: ∀ x such that x is an integer, x + 2 is an integer
symbol: ∃
meaning: “There is at least one”
example: ∀ x where x is an integer, ∃ y where y is an integer so that y > x
symbol: ∃!
meaning: “There is only one”
example: ∀ x where x is an integer, ∃! y where y is an integer and x-y = 1
symbol: ∈
meaning: “Is in” or “in,” depending on context.
example: ∀ x ∈ R, ∃ y ∈ R so that y > x (R is the set of real numbers)
symbol: A := B
meaning: “Let A equal B.” or “A, which has been defined to be equal to B,” depending on context.
example: A := R (The set A is defined to equal the set of real numbers)
symbol: s.t. or |
meaning: “Such that”/“So that”
example: ∀ x ∈ R, ∃ y ∈ R s.t. y > x
there are tons of other types symbols i can go over in the future like set and function notation if you guys are interested, but these logical symbols are crucial for reading proofs.