Real Numbers

"Geometry (which is the only science that it hath pleased God to bestow on mankind) ...
Leviathan 1651"

Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers.








They are called "Real Numbers" because they are not Imaginary Numbers

Examples: 2, 1/2, .5 , etc.

The Number Line

 A number line is normally drawn as a "long arrow", with integer numbers marked on it for reference. Negative numbers are to the left of zero, and positive numbers are to the right of zero.

Distance and Coordinates

 Distance

- absolute value of two points between the coordinates of the points.

Learnings:

♦Real Numbers have infinite examples.

 

♦It is divided into Rational and Irrational.

 

♦Rational comes from the word "ratio".

 

♦It can be any number that can be made from dividing one integer to another.

 

♦Examples are: 2, 1/2, 0.5, -29, etc.

 

♦Pi is an exception because it is an example of an Irrational Number.

 

♦An Irrational number defies the definition of a rational number. It is also a real number but it cannot be expressed as a ratio between two integers.

 

♦to find the distance between two points on a number line we use the distance formula:

♦The point that is exactly in the middle between two points is called the midpoint



 ♦For a number line with the coordinates a and b as endpoints:

Joseph-Louis Lagrange (1736 to 1813)

"As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection."

Sources:

http://www.mathsisfun.com/definitions/real-numbers.html

http://www.algebra.com/algebra/homework/Number-Line/what-is-number-line.lesson

 http://www.mathplanet.com/education/geometry/points,-lines,-planes-and-angles/finding-distances-and-midpoints

 

Absolute Value: Distance btwn two points