QM 1.ppt - Quantitative Methods by Dr Gyngyi Bugr Lectures...

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Quantitative Methods by Dr. Gyöngyi Bugár
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Lectures: Mondays: 11:00 – 12:15 Tutorials: Mondays: 12:30 – 13:45 Office Hours: Wednesdays: 12:30 – 13:45
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Brief review of the basic concepts of Mathematics: introduction to the theory of sets, numbers and functions ____________________________________ Set and element are basic concepts in mathematics. We do not define them. Sets are uniquely determined by their elements. Sets are denoted usually by capital letters A, B, C , etc. There are some standard notations : R denotes the set of real numbers, Q denotes the set of rational numbers, Z stands for the set of integers, N stands for the set of natural numbers (positive integers). The elements of a set are usually denoted by small letters, a, b, c, x, y, z , etc.
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Brief review of the basic concepts of Mathematics: introduction to the theory of sets, numbers and functions _____________________________________ Belonging to a set is denoted by the symbol ' '. (e.g., x, y, z R means that x, y and z are real numbers.) The symbol ' ' means that a given element does not belong to a given set. (e.g. Q , Q .) Empty set A set without any elements is called empty and denoted by Ø. Subsets A B denotes that any element of the set A belong to set B , as well. It is obvious that N Z Q R . 2
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Brief review of the basic concepts of Mathematics: introduction to the theory of sets, numbers and functions _____________________________________ Intervals Intervals are special subsets of R , the set of real numbers. Finite intervals: let a , b R be given such that a < b.
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