Inequação

Inequation: all literal inequation that is satisfied only by certain values​​, letters or incongnitas contained, in other words, it presents signs of greater (>) or less than (<) instead of the equal sign is that characterizes the equations.

Solutions or roots of an Inequality: the values ​​of the unknowns or letters that satisfy the inequality, which in turn nemerica inequality.

example:



It is essential for this theme that complemented inequalities are addressed by their graphs, is a complex issue that will take you to examine any kind of result.

Comparação de números inteiros

Comparison of integer numbers 

Compare and see which number is greater or less than another. 

Given the integers the least of them will be what is left on the line 

Examples 
And greater than -5 -15 -15 because this is the most left in the straight 
when in doubt, make straight 
5 + is greater than zero 
5 - less than zero and 
greater than zero and -10

Módulo de um numero inteiro

Modulus of an integer 
Modulus or absolute value of an integer is the distance to the source of his straight numerical examples ie zero modulo 4 -4 and 4 numbers until they are zero and your symbol and II 
and modulo zero and zero

Números inteiros opostos ou simétricos vamos considerar os pontos a e b na reta

Integer opposite or symmetrical
we will consider the points a and b on the line
_____A_4 Unidades____________4 unidades____________b_____
-4 -3 -2 -1 0 +1 +2 +3 +4
The points a and b are symmetric or opposite because they are the same distance
ie +4 and -4 are integers opposite or symmetrical
opposite 8 -: - (-8) = 8
opposite +5 = -5
and zero and symmetric himself

Representação geométrica dos números inteiros

We can represent integers in a reta.Usando the same unit of length, pointed to the right of the origin consecutive points and for each point, we match an integer positivo.Assim:


  ___________________ | __________________________
              0 +1 +2 +3 +4 +5


Note: Zero is always the origin of the line




We repeat this procedure for points located to the left of the origin, which do match the negative integers.


________ | __________________
      0 +1 +2 +3 +4 +5



We can meet in a single number line the positive integers and negativos.Essa line is called full number line.



_______________________________________________________________
                         -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5


                                   negative towards positive direction

Subconjunto de Z

See the definition of subset: A set A is a subset of set B if all elements of A are also elements B.Simplificando subset is one that has a set inside.




We will highlight, then some subset of Z and their representations.



Sets of natural numbers:
        | N = {0, +1, +2, +3, +4, +5, ...}


  Set of non-negative integers:
         Z + = {0, +1, +2, +3, +4 = 5, ...}


All non-zero integers
        Z * Z = {0} = {..., -3, -2, -1, +1, +2, +3, ...}



Set the positive integers:


       Z * = {+ +1, +2, +3, ...}


Set the non-positive integers:


       Z_ = {... -3, -2, -1,0}


Set the negative integers:


       _ * Z = {..., -3, -2, -1,0}


Remarks:



1-When you are positive numbers need not put the + sign.



56 = 56
78 = 78
+32 = 32

2-The asterisk which are the signs (| N *, Z * Z * + Z * _) means that zero does not belong to these conjuntos.Exemplos:


| N * = {+1, +2, +3, ...}
Z * _ = {... -3, -2, -1}

3-Z / + is set equal to the set | N; Z / + = | N


4 - | N is a subset Z /: | Z c N /

conjunto dos números inteiros

Belong to the set of integers, negative numbers and also the set of natural numbers, ie positive numbers.

The positive numbers to negative numbers are opposite and opposing negative to positive.
Their representation is made by the capital letter Z.

Z = {..., -4, -3, -2, -1, 0, +1, +2, +3, ...}

Remarks: negative numbers are always accompanied by a negative sign
(-) (In front) and positive are accompanied by a positive sign (+) or no sign. Zero is not positive nor negative.

♦ Whole non - null
Are the integers, less zero.
In its representation should put * next to the Z.
Z * = {... -3, -2, -1, 1, 2, 3, ...}

♦ positive integers not
Are negative numbers including zero.
In its representation should be placed - side to Z.
Z_ = {... -3, -2, -1, 0}

♦ not positive integers and non - null
Are integers from the set Z_ excluding zero.
In its representation we put _ and * next to the Z.
Z * _ = {... -3, -2, -1}

♦ non-negative integers
Are positive numbers including zero.
In its representation should put the + side of the Z.
Z + = {0,1, 2, 3, 4, ...}
The set Z + is equal to the set of N

♦ non-negative integers and non - null
Are the numbers of the set Z +, excluding zero.
In its representation should put the + and * next to the Z.
+ Z * = {1, 2, 3, 4, ...}
The set Z + * is set equal to N *