The closed interval [a,b] represents the set of all real numbers between a and b, including a and b. The table below lists nine types of intervals used to describe subsets of real numbers. Notice the number line representation of each interval. Basically, an interval is a set containing all numbers between two given numbers or endpoints.
The set may have one, both, or neither of the two given numbers. An interval is open if the interval does not contain its endpoints. The symbols or are used to indicate that an endpoint is not included in the interval. An interval is closed if the interval contains its endpoints. The symbols [ or ] are used to indicate that an endpoint is included in the interval. Sometimes, the interval may contain only one of its endpoints.
In this case, the interval is half-open. In particular, factoring a number means to break it down into numbers that when multiplied back together produce the given number. For now, we will focus on factoring whole numbers. For example, consider the number To find the factors, consider the numbers that yield a product of If we think about it, we can list all of the numbers that 24 is divisible by: 1, 2, 3, 4, 6, 8, 12, and This is a complete list of the factors of Prime factorization example: This factor tree shows the factorization of It shows that is the product of five 2s and three 3s.
Prime factorization is a particular type of factorization that breaks a number of interest into prime numbers that when multiplied back together produce the original number. Such prime numbers are called prime factors. For example, consider the number 6. Also note that 2 and 3 are prime numbers, because each is divisible by only 1 and itself.
Therefore, 2 and 3 are prime factors of 6. Now, consider the number However, 6 is not a prime factor. In this case, we must reduce 6 to its prime factors as well. We have now found factors for 12 that are all prime numbers.
Every positive integer greater than 1 has a distinct prime factorization. To factor larger numbers, it can be helpful to draw a factor tree. This is expressed using closed interval notation: [-3,1]. This type of interval includes only one of the endpoints of the inequality.
This is expressed using half-open interval notation: [-3,1. We can follow certain rules and symbols to represent the interval notation for different types of intervals. Let us understand different symbols that can be used to write a particular type of interval. Different types of interval notation can be represented on a number line. Look at the handy table that distinguishes between all the types of intervals using their representation on a number line.
Example 1: For a person to be elected as the president, he should be a minimum of 35 years old. Give an interval representing this information. Example 2: For a school to participate in an Olympiad exam, the number of students from the school should be a minimum of Represent this using an interval notation.
Let x represent the number of students participating in a class, then x should be greater than or equal to Example 3: Lola needs at least calories a day but the calorie intake should not exceed calories. Those two methods complement each other when working with inequalities.
The latter method make visualizations straightforward. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Interval Notation - What is the purpose? Ask Question. Asked 9 years, 2 months ago. Active 10 months ago. Viewed 3k times. Kartik Audhkhasi 1, 7 7 silver badges 12 12 bronze badges.
0コメント