Set Notation
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High Quality Content by WIKIPEDIA articles! Sets are fundamental objects in mathematics. Intuitively, a set is merely a collection of elements or members. There are various conventions for textually denoting sets. In any particular situation, an author typically chooses from among these conventions depending on which properties of the set are most relevant to the immediate context or on which perspective is most useful. A notable exception to the braces notation is used to express intervals on the real line. Any such interval is well defined only because the real numbers are totally ordered.…mehr

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High Quality Content by WIKIPEDIA articles! Sets are fundamental objects in mathematics. Intuitively, a set is merely a collection of elements or members. There are various conventions for textually denoting sets. In any particular situation, an author typically chooses from among these conventions depending on which properties of the set are most relevant to the immediate context or on which perspective is most useful. A notable exception to the braces notation is used to express intervals on the real line. Any such interval is well defined only because the real numbers are totally ordered. It is completely determined by its left and right endpoints: the unit interval, for instance, is the set of reals between 0 and 1. The convention for denoting intervals uses brackets and parentheses, depending as the corresponding endpoint is included in or excluded from the set, respectively. Thus the set of reals with absolute value less than one is denoted by (-1, 1) note that this is verydifferent from the ordered pair with first entry -1 and second entry 1.