Closure properties of numbers

comprehensive explanation of numbers property

1. F.Sc MATH

2. A Self-Tutorial Presentation of SKY HAWKS’ ACADEMY By Professional Mathematics Tutors

3. CLOSURE PROPERTY OF NUMBERS

4. that when you perform an operation ( such as addition, multiplication, etc )

5. on any two numbers in a set, the result of the computation is another number in the same set

6. Real numbers are closed with respect to addition and multiplication

7. Example 1 Adding two real numbers produces another real number Math - Adding Real Numbers = Another Real Number The number "21" is a real number.

8. Example 2: Multiplying two real numbers produces another real number Math - Mult Real Numbers = Another Real Number The number "312" is a real number. .

9. When the term "closure" is used in mathematics, it applies to sets and mathematical operations

10. The sets can include ordinary numbers, vectors, to matrices, algebra, and other elements.

11. The operations can include any operation (addition, multiplication, square root, etc.).

12. However . . . here, our concern is only with the closure property as it applies to real numbers

13. Why is this important to know?

14. It is important because equations which only involve addition and multiplication have a solution which is also a real number - you know that in advance.

15. For example, you know for certain that you can add the costs of all the items in a shopping basket and get a "real number" answer. This is due to the property of closure.

16. This is because the definition of an even number is it can be written as 2 multiplied by a whole number.

17. If this were not the case, you could never be sure that addition would quite work.