The “such that” statment is denoted by the colon symbol and represents a condition placed on the expression that comes before the colon. For example, the following expression which defines the set of complex numbers contains a “such that” expression within it.
In plain language, this means that a member of exprssion such that and belong to the set of real numbers and .
The element of symbol describes membership to a set. When reading an equation the symbol can be read as "in" or "belongs to".
A set is written with curly braces containing the elements of the set separated by commas.
The syntax for "there exists" is a backwards captial E. It is often used in conjuction with a variable with certain properties.