diff --git a/06-hash/hash.tex b/06-hash/hash.tex index 7e12db329ecee5b6ebeec0a2313b516f22d449e6..54efa1185be6c8a6dc46e4c690f59da58e691e8c 100644 --- a/06-hash/hash.tex +++ b/06-hash/hash.tex @@ -134,7 +134,7 @@ ${\cal L} = \{ h_{a,b} \mid a,b\in [p] \}$ from $[p]$ to $[m]$, where $h_{a,b}(x) = ((ax+b) \bmod p) \bmod m$. } -\theorem{The family~$\cal L$ is 1-universal.} +\theorem{The family~$\cal L$ is 2-universal.} \proof Let $x,y$ be two distinct numbers in $[p]$. diff --git a/08-string/string.tex b/08-string/string.tex index b92156c73fb7467cce5711118d78d064593f4a70..a2ccb5e10d6a2717d27d4054864290515ee70863 100644 --- a/08-string/string.tex +++ b/08-string/string.tex @@ -20,7 +20,7 @@ are indexed starting with~0. \:$\alpha[i:j]$ is the \em{substring} $\alpha[i]\alpha[i+1]\ldots\alpha[j-1]$; note that $\alpha[j]$ is the first character \em{behind} the substring, - so we have $|\alpha[i:j]| = j-i$. If $i>j$, the substring is empty. + so we have $|\alpha[i:j]| = j-i$. If $i\ge j$, the substring is empty. Either $i$ or~$j$ can be omitted, the beginning or the end of~$\alpha$ is used instead. \:$\alpha[{}:j]$ is the \em{prefix} of~$\alpha$ formed by the first~$j$ characters.