Real Number System

The natural numbers, or counting numbers, are the positive integers:

1, 2, 3, 4, 5, . . . . The negative integers are -1, -2, -3, . . .. .

A number in the form a/b, where a and b are integers, b ­ 0, is a rational number. A real number that cannot be written as the quotient of two integers is called an irrational number, e.g., , , , Π, e, .

There is a one-to-one correspondence between the set of real numbers and the set of points on an infinite line (coordinate line). Order among Real Numbers; Inequalities

a > b means that a - b is a positive real number.
If a <>
If a <>
If a <> 0, then ac <>
If a <> bc.
If a <>
If 0 <>
If a <> 0, then 1/a > 1/b.
If a <>

Absolute Value For any real number x, |x| = if x ³ 0, -x if x <>

Properties

If |x| = a, where a > 0, then x = a or x = -a.
|x| = |-x|; -|x| ≤ x ≤ |x|; |xy| = |x| |y|.
If |x| <> 0.
||x| - |y|| ≤ |x + y| ≤ |x| + |y|.
= |x|.

Comments

Post a Comment

Popular posts from this blog

Cube and Tube Formula

Image
Cube: Cube Volume V = a 3                              (1) where V = volume (m 3  , ft 3  ) a = side (m, ft) Surface Area Ao = 6 a 2   (1b) where Ao = surface area (m 2 , ft 2 ) Diagonal d = a 3 1/2  (1c) where d = innside diagonal (m, ft) Cuboid Tube Volume V = a b c                                    (2) where: V = volume of solid (m 3  , ft 3  ) a = length of rectangular prism (m, ft) b = width of rectangular prism (m, ft) c = height of rectangular prism (m, ft) Diagonal d = (a 2 + b 2   + c 2 ) 1/2                    (2b) Surface Area Ao = 2 (a b + a c + b c)                 (2c) where Ao = surface area of solid (m 2 , ft 2  ) Parallel piped: Parallel Pipped Volume V = A 1 h (3a) where A 1 = side area (m 2 , ft 2  ) Cylinder: Cylinder Volume V = π/4 d 2   h = π r 2 h         (4a) where d = diameter of cylinder (m, ft) r = radius of cylinder (m, ft)
Read more

Statistic Problem

1. Known the number of ball n(s) = 100 Ask: The change take a ball with number divisible by 5 but not divisible by 3 if taken randomly. Answer: For example A = ball with number divisible by 5 but not divisible by 3 n(A) = 14, namely 5, 10, 20, 25, 35, 40, 50, 55, 65, 70, 80, 85, 95 and 100 P(A) = n(A)/n(s) = 14/100 = 7/50 2. Known: One badminton team consist of 5 members, will decide 2 people play a single players, and 2 pairs to play double. Ask: How many option can be made. First Way Solution: For example 5 people of badminton team are A, B, C, D, and E. Then we choose A and B to play single. Option Single Double 1 A, B CD, AE 2 A, B CE, AD 3 A, B  DE, AC 4 A, B CD, BE 5 A, B CE, BD 6 A, B DE, BC The option number when A and B choose as single player are 6 option. The way to choose player as single player are 10, namely AB, AC, AD, AE, BC, BD, BE, CD, CE, and DE. From one option of single player will make 6 option so for all way to choose single
Read more

Phytagoras Formula

Image
A simple formula from pythagoras is calculatef of each side on right triangle as follows: C 2 = A 2 + B 2 Where : C = the incline side length A and B = other triangle side length. For Example calculation can see on picture below: For your excercise please do the following problem: Calculate the length of the hypotenuse if the lenght elbow side 6 and 8? Calculate the length of one side of the elbow if the length of the hypotenuse = 10 and the other 4?
Read more