i'm having a lot of trouble figuring out when to use a closed or an open interval.
do i use infinity in every question where both numbers are not defined?
insight?
thanks/
If no lower or upper or lower limit of an interval is specified, assume it is infinity (+ or -)
Use an open when the sign is NOT including the anwser. Use a closed when the sign DOES include the answer.
Infinity is used when you have PARAELL lines.
how can i tell if something is included or not?
the answers i'm getting are like:
z>-3
which is the correct answer. but when i go to graph it in the computer, i always click the wrong representation of interval notation.
The red arrow shows that all the values on the number line less than –3 are in the solution. The open circle at –3 shows us that –3 is not in the solution.
Like this? Why is -3 not in the solution? How can I tell?
Understanding when to use a closed or an open interval can be tricky at first, but with some explanation, it should become clearer.
An open interval does not include its endpoints, while a closed interval does include them. To determine which one to use, you need to consider the context and what is required or specified in the problem.
For example, suppose we have the inequality x > 2. If you need to find the solution set in interval notation, it will be (2, ∞). Notice that the interval is open on the left because x cannot equal 2 (only values greater than 2 are allowed), and it is open on the right because there is no upper bound specified.
On the other hand, if you have the inequality x ≥ -4, the solution set in interval notation will be [-4, ∞). In this case, the interval is closed on the left because x can equal -4, and it is still open on the right because there is no upper bound specified.
Now, when it comes to using infinity (∞), it is not necessary to include it in every question where both numbers are not defined. Infinity is typically used when an interval extends indefinitely in one or both directions. For example, if you have the inequality x ≤ 5, the solution set in interval notation will be (-∞, 5]. Here, the interval is open on the left because there is no lower bound specified, and it is closed on the right because x can equal 5.
In summary, determining whether to use a closed or an open interval depends on the specific problem and its requirements. Pay attention to the given conditions and what values are or are not allowed, and choose the appropriate type of interval notation accordingly.