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TECNOLÓGICO DE MONTERREY


Mathematics Department - VEM

Real Numbers

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Sets

The conceptof a set is fundamental in all branches of Mathematics. Intuitively, a set is a list, collection or class of objects that are well defined, which can be: numbers, cars, letters, people’s names,ages, etc. The objects that make up a set are called elements or members of the set.


Examples:


1. Vowels in the alphabet: a, e, i, o, u.
2. Even positive numbers: 2, 4, 6, 8,. .. .
3. Prepa Tec Mathematics I students who are taller than 170 cm.
4. red, blue, green.

Notation:
- It is common to use capital letters (A,B,X,Y, . . .) to represent the name of aset, and lowercase letters are used for elements (a,b,x,y, . . . ) and this ones should NOT be repeated
- Keys or curly brackets are used to write out sets, including the elements or adescription between them Example: {1, 7, 16, 25, 30,39,....}
- If x is an element of set B, it is noted as [pic] and if it is not an element of B it is noted as [pic].


Numerical Sets:The following sets are commonly used to denote groups of defined numbers
Natural numbers or Positive Integers (N or Z+) = [pic]Negative Integers ( Z- ) = [pic]
Whole numbers (W) = [pic]

Integers (Z) = [pic]
Rational numbers (Q) = [pic]
Irrational numbers (Q´) = [pic]


Real numbers(R) = [pic]

Examples:
Write out the following sets by roster form, if possible:
a) [pic]
b) [pic]
c) [pic]

Answers:
a) [pic] b) [pic] c) Cannot be expressed-----------------------




Natural Numbers


Zero

Negative Integers

Whole Numbers

Non- integer Numbers

Integer Numbers

Irrational Numbers

Rational Numbers

Real Numbers