Chapter 1



Section 1.6

Numerical sets

Sets of Natural Numbers

Representation: N = {0, 1, 2, 3, 4, 5, ...}

Subset:
A very represented subset of the natural numbers is one where the zero element does not exist.
The letter N is accompanied by an asterisk (*).

Example: N * = {1, 2, 3, 4, 5, ...}

Graphic representation:





Whole Number Sets

Representation: Z = {...- 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}

Subset: A well-represented subset of integers is one where zero is not present.
The letter Z is marked with an asterisk (*).

Example:
Z * = {..., - 3, -2, -1, 1, 2, 3, ...}

Another example is the subset of nonnegative integers.

Representation:
Z + = {0, 1, 2, 3, ...}

Finally, there is also the subset of non-positive integers.

Representation:
Z_ = {...- 3, -2, -1, 0}

Graphic representation of the set of integers:





Sets of Rational

Definition:



Examples:

3/4, 5/6, 7/8, 11/5, -3, 2, 0, 7.

Every rational number can be written in the form a / b.

Examples:

A) -3 = -3/1
B) 0 = 0/10

Rational numbers are divided into exact or finite decimals.

Examples:

A) 2/5 = 0.4
B) 100/25 = 4



Periodic or infinite decimals

Examples:

A) 1/3 = 0.333 ...
B) 10/3 = 3.333 ...

Graphical representation of the rational set:





Sets of Irrational Numbers

Irrational numbers are those that can not be represented as a / b (rational)

Examples:



Irrational numbers form non-periodic tithe.

Graphic representation:





Real Number Sets

Definition:



Venn diagram for the set of real numbers:



Subassemblies of the real numbers:
A) R * = R - (0)
B) R + = set of non-negative real number
s
C) R_ = set of non-positive real numbers

Graphic representation:



The real numbers fill all the points of the straight line above. Therefore, this line is called the real line.




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