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1.4

Glossary

# Glossary

We are planning to prepare a Glossary for the course that contains a list of the key terms that are used in the course.

Which terms would you like us to explain here?

## Symbols

$$:=$$ Equal by definition. E.g., for any real number $$a\in \mathbb R$$ one has $$a^2:= a\cdot a$$.

$$\exists$$ :There exists.

$$\in$$: Belongs to

$$\subset$$: Is a subset of

$$\forall$$: For every

$$\mathbb N$$: The set of natural numbers $$0,1,2,3,…$$.

$$\mathbb Q$$: The set of rational numbers.

$$\mathbb R$$: The set of real numbers.

$$\mathbb Z$$: The set of integer numbers $$…,-3,-2,-1,0, 1,2,3,…$$: $$\mathbb N\subset\mathbb Z\subset\mathbb Q\subset\mathbb R$$

## I

Integer: a number of the set $$\mathbb Z=\lbrace …,-3,-2,-1,0,1,2,3,…\rbrace$$

## N

Natural number: a number of the set $$\mathbb N=\lbrace 0,1,2,3,…\rbrace$$

## R

Rational number: a number of the set $$\mathbb Q=\left\lbrace \dfrac ab:\, a\in\mathbb Z, b\in\mathbb Z\setminus\lbrace 0\rbrace\right\rbrace=\left\lbrace \dfrac ab:\, a\in\mathbb Z, b\in\mathbb N\setminus\lbrace 0\rbrace\right\rbrace$$

Real number: an element of $$\mathbb R$$. The set $$\mathbb R$$ contains the limits of sequences of rational numbers and elements like square roots, $$\pi, e,…$$

## S

Square root of $$x\ge 0$$: the positive number $$y$$ satisfying $$y^2=x$$.

$$m-$$th root of $$x\ge 0$$: the positive number $$y$$ satisfying $$y^m=x$$.

## Get a taste of this course

Find out what this course is like by previewing some of the course steps before you join:

• ##### Alberto and Carlo explain the course structure
video

Alberto and Carlo explain the course structure

video

Integers

• ##### Rational numbers
video

Rational numbers

video

Real numbers

• ##### Absolute value
video

Absolute value

• ##### An induction proof
video

An induction proof

• ##### The function concept
video

The function concept

• ##### The graph of a function
video

The graph of a function

• ##### Integer powers
video

Integer powers

• ##### Roots and radicals
video

Roots and radicals

• ##### Simplifying radicals
video

Simplifying radicals

• ##### Rational powers
video

Rational powers

• ##### Polynomial and identities
video

Polynomial and identities

• ##### Roots of polynomials
video

Roots of polynomials

• ##### Roots of quadratic polynomials
video

Roots of quadratic polynomials

• ##### The Euclidian division algorithm
video

The Euclidian division algorithm

• ##### Finding roots
video

Finding roots

• ##### Binomial coefficients
video

Binomial coefficients

• ##### Introduction: types of equations
video

Introduction: types of equations

video

Equivalence

• ##### Polynomial equations
video

Polynomial equations

• ##### Equations involving a radical
video

Equations involving a radical

• ##### Equations with several radicals
video

Equations with several radicals

• ##### Equations with absolute values
video

Equations with absolute values

video

Systems

video

video

• ##### The quadratic case
video

The quadratic case

• ##### Polynomial inequalities
video

Polynomial inequalities

• ##### Inequalities with one radical
video

Inequalities with one radical

• ##### Inequalities with absolute values
video

Inequalities with absolute values

• ##### Lines in the plane
video

Lines in the plane

• ##### Systems of linear inequalities
video

Systems of linear inequalities