i am doin homework and i do not know what an interval is
An interval is to indicate a range of values on the number line.
For example, if we want to say:
0≤x≤10, we would say that
x is on the interval [0,10], where 0 and 10 are the limits of the interval, and [] stand for the ≥ and ≤ signs respectively.
If the limit is excluded from the interval, such as 0≤x<π
we write:
[0,π)
Same goes for
-∞<x<∞, or (-∞∞).
All this sound abstract, the best is to post a relevant question, which demonstrates the context of what you are doing in your course.
Enter the interval [-4,oo)
An interval is a concept used in mathematics to describe a range of numbers. It represents all the numbers between two endpoints, including the endpoints themselves. The interval can be either inclusive (including the endpoints) or exclusive (excluding the endpoints). Here are a few examples to help you understand it better:
1. Closed Interval: [a, b]
This interval includes both endpoints a and b. For example, the closed interval [2, 6] consists of all numbers starting from 2 and going up to 6, including both 2 and 6.
2. Open Interval: (a, b)
This interval does not include the endpoints a and b. For example, the open interval (2, 6) consists of all numbers greater than 2 and less than 6, but not including 2 and 6 themselves.
3. Half-Open Intervals: [a, b) or (a, b]
These intervals include one endpoint but not the other. For example, the half-open interval [2, 6) includes 2 and all numbers up to, but not including 6.
To understand intervals better, it's always helpful to visualize them on a number line. Plotting the endpoints and shading the region in between will give you a clear idea of what numbers are included in the interval.