Interval NotationDate: 06/25/97 at 13:32:27 From: Paige Wade Subject: Pre-Calculus (Algebra) Can you please send me the rules for writing answers in interval notation? Date: 06/28/97 at 15:21:49 From: Doctor Mark Subject: Re: Pre-Calculus (Algebra) Hi Paige, First of all, interval notation always has two numbers: one on the left, and another on the right, separated by a comma. (I don't want the Math Police to come after me, so I'd better say this also: infinity is not a number.) The number on the left has to be less than the number on the right. If the number on either the left or the right is included in the interval, you use a left (if it's the number on the left) square bracket "[" or a right (if it's the number on the right) square bracket "]" If the number is not included in the interval, you use a parenthesis "(" on the left and ")" on the right. These also correspond to the inequality symbols: if it's "<" or ">" use a parenthesis, and if it's "<=" (less than or equal to) or ">=" (greater than or equal to) use a square bracket. Some examples: If a < x <= b, you write (a, b], since a is not included in the interval (x has to be greater than a, so it can't equal a, and therefore it's not included in the interval), but b is included (because x could equal b). If a <= x <= b, you write [a, b], since a and b are both included in the interval (x could be equal to either a or b). If a <= x < b, you write [a, b), since a is included in the interval, but b isn't (x could equal a, but it can't equal b, since it is less than b). If a < x < b, you write (a, b), since neither a nor b is included in the interval (x can't equal a because a is less than x, and x can't equal b because x is less than b). Those are the only 4 possibilities. But there's a catch: If an a or b above is infinity (or minus infinity), then you have to use "(" or ")" next to the infinity, since no x can equal infinity because infinity is not a number. So you can never have anything like (- 5, infinity]. Hope this helps. If not, write back. -Doctor Mark, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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