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\begin{document}

\title{Episode AP04\\ Different kinds of numbers}
\subtitle{European section, Season 1}
\author{}
\date{}

\Large


\begin{frame}
  \titlepage
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\begin{frame}
\begin{block}{Natural numbers}\pause
A \textbf{natural number} is one that can be found in nature. It has no decimal part and no sign. The smallest natural number is $1$.
\end{block}\pause

Examples : $2$ ; $67$ ; $10989$ 
\end{frame}

\begin{frame}
\begin{block}{Whole numbers}\pause
A \textbf{whole number} is a positive number with no decimal part.
\end{block}\pause

Examples : $5$ ; $436$ ; $0$ 
\end{frame}

\begin{frame}
\begin{block}{Integers, negative, positive}\pause
An \textbf{integer} is just a number with no decimal part. It's \textbf{positive} (sign $+$) if it's greater than $0$ and \textbf{negative} (sign $-$) if it's lower than $0$.
\end{block}\pause

Examples : $-756$ ; $+10$ ; $-77$ 
\end{frame}

\begin{frame}
\begin{block}{Even numbers}\pause
An integer is \textbf{even} if it's \textbf{divisible} by $2$, or equivalently if it can be cut in two equal integer parts.
\end{block}\pause

Examples : $2$ ; $52$ ; $-7008$ 
\end{frame}

\begin{frame}
\begin{block}{Odd numbers}\pause
An integer is \textbf{odd} if it's not even, that is if it's not a \textbf{multiple} by $2$.
\end{block}\pause

Examples : $-3$ ; $17$ ; $101$ 
\end{frame}

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\begin{block}{Prime numbers}\pause
A whole number is \textbf{prime} if it's only positive divisors are $1$ and itself.
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Examples : $7$ ; $31$ ; $47$. 
\end{frame}

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\begin{block}{Decimal numbers}\pause
A \textbf{decimal number} is a number whose \textbf{decimal part}, the part on the right-hand side of the \textbf{decimal point}, is made of a finite number of \textbf{digits}.
\end{block}\pause

Examples : $12$ ; $-7.52$ ; $15.51$ 
\end{frame}

\begin{frame}
\begin{block}{Rational numbers}\pause
A \textbf{rational number} is a number which can be expressed as a ratio of two integers. Non-integer rational numbers (commonly called \textbf{fractions}) are usually written as the vulgar fraction $\frac{a}{b}$, where $b$ is not zero. $a$ is called the \textbf{numerator}, and $b$ the \textbf{denominator}.
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Examples : $\frac{17}{3}$ ; $-45$ ; $-\frac{47}{5}$ 
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\begin{block}{Irrational numbers}\pause
An \textbf{irrational number} is any real number that is not a rational number -- that is, it is a number which cannot be expressed as a fraction $\frac{m}{n}$, where $m$ and $n$ are integers, with $n$ non-zero.
\end{block}\pause

Examples : $\pi$ ; $\sqrt{2}$ ; $e$ 
\end{frame}

\begin{frame}
\begin{block}{Real numbers}\pause
The \textbf{real numbers} can be described informally as numbers with an infinite decimal representation. The real numbers include the rational numbers and the \textbf{irrational numbers}.
\end{block}\pause

Examples : $42$ ; $-\frac{23}{129}$ ; $\pi$
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