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When a = b, interval ( a, a ) : =  and [ a, a ] : = { a }. Intervals of the type (a ,b ] are called left-open right-closed intervals. |
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Simililarly, intervals of the type [ a, b ) are called left-closed right-open Intervals. And intervals of the type ( a, b ), ( - , a ), ( a, + ) are called open intervals and of the type [ a,b ], ( -,a ], ( a, + } are called closed intervals. Note that -, + are just symbols, and not numbers.
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As stated above, shall assume that the set of real numbers can be identified with points on the straight line.
If point O represent the number 0, then points on the left of O represent negative real numbers and points on the right of O represent positive real numbers. Intervals are part of the line as shown: |
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This identification is useful in visualizing various properties of real numbers. An open interval of the type
( ) is called an  - neighborhood of a   . |
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