Marked 01/02/09

Created By: Tanya,Brad,Liam,Michael

Number Sets Are A Way To Distinguish Between Different Kinds Of Numbers.

There are 6 basic Number Sets, And 1 not so basic Number Set...

Basic:



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Integers



Examples:



...-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...



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Integers Are All Negative And All Postitve Numbers. That includes 0.



Symbol

Z


Natural Numbers



Examples:



1,2,3,4,5,6,7,8,9,10 ...



Natural Numbers Are All Numbers Starting from 1 and going on forever. Does Not Include Negative Numbers or Zero.


Symbol

N


Whole Numbers



Examples:



0,1,2,3,4,5,6,7,8,9,10...



Whole Numbers are any numbers starting from zero.It does not iclude negatives, and decimals

Symbol




W


Rational Numbers



Rational numbers are number that can b used as ratio of two integers, where the divisor is not 0 and rational numbers are numbers in the form A/B, where b cannot be zero. It includes all fractions, all integers, all terminating decimans and all repeating decimals.



What is a termiating Decimal??



Termingating Decimals are numbers with decimals theat end (0.25, 3.07, 0.19 etc...)



Not A number with a decimal that never ends (0.641841548169542195632...............)



Symbol

Q

Irrational Numbers (ugly numbers)

Irrational Numbers are a number that cannot be written as a ratio of two integers/cannot be expressed and irrational numbers are not rational. They are numbers that can not be expressed as fractions and have niether terminating nor repeating decimals. irrational numbers are numbers that never end thats why they are ugly. When a test asks you for an irrational number to remember think of pie 3.141592654 and so on.

Examples-

Pie, Square root of 2, square root of 3

Symbol




~

Q

Real Numbers



Every number that you know

Includes all of the other number sets.

Real Numbers are the top of the diagram. This is because everything below Real Numbers is a Real number. Real numbers can also have a negative value and factions which includes every number you know . They don't always have to be a positive number or a decimal number. On a test if your thinking real numbers every number is real there is no fake numbers.

Symbol

R

Examples: 1, 7, 6, 4, -5 ,1.567, 45.54, 78, 125.784 etc...

Not so basic...

Complex



complex numbers are extensions of real numbers obtained by joining an imaginary unit.



every complex number can be written in a + bi form. A and B are the real numbers part of the equation and the imaginary part of the complex number.



Imaginary Unit is denoted by i. It is often referred to as the Square Root Of -1. Or the square root of minus 1.



x2+1

0=



Since there is no REAL number that produces a negative real number when squared, we imagine such a number and assign it the letter i.

Symbol Study Techniques

Real Numbers - The R in Real is the symbol

Rational Numbers- *no study technique* Q

Irrational Numbers- The same as Rational (Q) but with a special touch (~) ~

Q

Integers- The S at the end sounds like a Z (integerzzzzz) and a flipped S is Z

Whole- The W at the beginning of Whole is the symbol W

Natural- The N At the beginning of Natural is the symbol N

Review Test!


1. State Whether Each Data Is An Integer, Natural, Whole, Rational, Irrational or Real Number. If more than one apply, write all that apply.(won't have any exaples of complex)

a.) -2/3

b.)13

c.) 1.3425647267932965739

d.) -1

e.) -6.8

f.) square root of 15

2. TRUE OR FALSE

a.) a real number is also rational, irrational, integers, whole, natural T F

b.) if a number is an integer is also a whole number T F

c.) if a number is irrational, then it must also be an integer T F

d.) if a number is irrational, then it must also be a real number T F

Write The Symbol

a.) irrational numbers

b.) whole numbers

c.) real numbers

d.) rational numbers

e.) natural numbers

f.) integers

Answers


1. a.) Rational, Real

b.) Integers, Natural, Rational, Real, Whole

c.) Irrational, Real

d.) Integers, Rationl, Real

e.) Rational, Real

f.) Irrational, Real

2. a.) true

b.) false

c.) false

d.) true

3. a.) ~Q

b.) W

c.) R

d.) Q

e.) N

f.) Z

Works Cited

Complex Numbers Information --> http://en.wikipedia.org/wiki/Complex_number

MATHPOWER9