The traditional division of mathematics into subdisciplines is as follows. Arithmetic—The study of whole numbers and fractions. Sample theorem: If you subtract an odd number from an even number you get an odd number. Geometry—The study of figures in space—points, lines, curves, and three-dimensional objects. Sample theorem: The angles of a triangle on a flat surface add up to 180 degrees. Algebra—The use of abstract symbols to represent mathematical objects (numbers, lines, matrices, transformations), and the study of the rules for combining those symbols. Sample theorem: For any two numbers x
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