\title{Epsilon - Delta}
\language{en}
\range{-0.9..0.9}
\author{Gang XIAO}
\email{xiao@unice.fr}
\computeanswer{yes}
\format{html}
\precision{10000}

\integer{center=random(1..50)}
\integer{r1=random(0,1)}
\integer{r2=random(0,0,1)}
\integer{r3=random(0,0,1)}
\text{D1=\r1=0?\varepsilon:\delta}
\text{D2=\r1=0?\delta:\varepsilon}
\text{E1=\r2=0?\D2:\D1}
\text{E2=\r2=0?\D1:\D2}
\text{C1=\r3=0?x-\center:f(x)-f(\center)}
\text{C2=\r3=0?f(x)-f(\center):x-\center}
\text{cont=That f is continuous on \center}
\text{noncnt=That f is not continuous on \center}
\text{unknown=Does not determine the continuity of f}
\text{bad=\cont, \noncnt, \unknown}
\text{good=\r2=0 and \r3=0?\cont:\unknown}

\statement{Let \(f: \RR \rightarrow \RR) be a real function such that:
<p><center>
 For all \(\E1>0), there exists a \(\E2>0) such that \(|\C1|<\D1) implies
 \(|\C2|<\D2).
</center></p>
What does this mean to the continuity of \(f)?
}

\choice{Signification}{\good}{\bad}


