From: Christoph Fuerst Date: Sun, 4 Jun 2017 08:14:35 +0000 (+0200) Subject: corrected wrong statement about sets X-Git-Url: http://git.risc.jku.at/gitweb/?a=commitdiff_plain;h=6868ef67201e60f7c0be9138e45ccd0de0f0695f;p=cfuerst%2Fformal-numbers.git corrected wrong statement about sets --- diff --git a/report/formal.tex b/report/formal.tex index 03d97de..9d7f9f5 100644 --- a/report/formal.tex +++ b/report/formal.tex @@ -422,15 +422,16 @@ and this descent can only be performed finitely often. \subsection{The Sieve of Erathostenes II} -In modern programming languages, such as C, \CC and Java, one distinguishes between \emph{primitive datatypes}, +In modern programming languages, such as C and Java, one distinguishes between \emph{primitive datatypes}, and \emph{compound datatypes}. For example, in C one can consider \texttt{char}, \texttt{int}, \texttt{long}, \texttt{float} and \texttt{double} as primitive datatypes. If data elements consist of multiple values, e.g. a playing card consisting of its numerical value and its suit, on can use the concept of \texttt{struct}, which is a first example of a compound datatype. -In \CC and Java one can additionally use the object oriented concept of \emph{classes}.\\ +In Java one can additionally use the object oriented concept of \emph{classes}.\\ However, in either case the mathematical category of \emph{set} is not in the standard instruction set available and -a programmer who wants to use sets is in position to implement the data structure and hence produces a source of errors -in the final program. To that end, programmers might prefer the second representation of the Sieve of Erathostenes, +a programmer who wants to use sets is in position to implement the data structure. The closest description is by the +\CC standard template library (STL), which provides the data structure set of +To that end, programmers might prefer the second representation of the Sieve of Erathostenes, that we are going to develop in this section.\\ Suppose, we want to answer question \eqref{eq:q1} for a nonnegative integer $n>2$.