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| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 2.2 | Upper and Lower Bounds. Intervals and Segments |
In these revision notes for Upper and Lower Bounds. Intervals and Segments, we cover the following key points:
By definition, the lower bound is the smallest actual value that gives a certain rounded number, while the upper bound is the largest actual value that gives the same rounded number.
We can use approximations during the rounding process to quickly estimate value of an expression.
The concepts of upper and lower bound are applied in practice to confirm the minimum and maximum value of an item. The lower and upper bound of a value are expressed in a value that is of a one position higher precision that the rounded value.
An interval is a set of numbers in which all values are included except the bounds. It is expressed through curved brackets, ().
A Segment on the other hand, represents a set of numbers that include the "in-between values" and the two bounds as well. A segment is expressed through the square brackets [ ].
Intervals are shown on the number line by white (empty) dots while segments are depicted by black (filled) dots. We say the ends of an interval are open while those of a segment are closed.
On the other hand, when the lower bound (the left end) is open and the upper bound (the right end) if closed, we have a half-interval. Likewise, when the lower bond (the left end) is closed and the upper bound (the right end) is open, we have a half-segment.
When one end of a number set extends to infinity, we represent that part using the symbol of interval as it is impossible to find the exact value of infinity.
We use the concept of half-segment to indicate the possible values of a number which, when rounded, provide the same value. In this situation, the number included in the lower bound is included in the set while after the upper bound there is always an "uncovered" part, which is dictated by the precision of numbers involved.
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