The document discusses the closure property of real numbers. It explains that when you perform addition or multiplication on real numbers, the result will always be another real number. This is an important property because it means equations involving only addition and multiplication are guaranteed to have a real number solution. The closure property ensures operations like adding costs in a shopping basket will always yield a real number total.

2. F.Sc MATH

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

4. CLOSURE
PROPERTY
OF
NUMBERS

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

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

7. Real numbers
are closed with
respect to
addition and

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

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

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

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

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

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

14. Why is this
important to
know?

15. 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.

16. 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.

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

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