Describe the uses of the following symbols { }, [ ], and ( ) in mathematics. What are two different and sometimes confusing uses of ( ) in mathematics.

A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entierely constitued with symbols of various types, many symbols are needed for expressing all mathematics.

The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other sort of mathematical objects. As the number of these sorts has dramatically increased in modern mathematics, the Greek alphabet and some Hebrew letters are also used. In mathematical formulas, the standard typeface is italic type for Latin letters and lower-case Greek letters, and upright type for upper case Greek letters. For having more symbols, other typefaces are also used, mainly boldface {\displaystyle \mathbf {a,A,b,B} ,\ldots ,}{\displaystyle \mathbf {a,A,b,B} ,\ldots ,} script typeface {\displaystyle {\mathcal {A,B}},\ldots }{\displaystyle {\mathcal {A,B}},\ldots } (the lower-case script face is rarely used because of the possible confusion with the standard face), German fraktur {\displaystyle {\mathfrak {a,A,b,B}},\ldots ,}{\displaystyle {\mathfrak {a,A,b,B}},\ldots ,} and blackboard bold {\displaystyle \mathbb {N,Z,R,C} }{\displaystyle \mathbb {N,Z,R,C} } (the other letters are rarely used in this face, or their use is controversial)

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