Wrestling with the Fundamental Theorem of Calculus
Wrestling with the Fundamental Theorem of Calculus
Wrestling with the Fundamental Theorem of Calculus
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Riemann’s function: f( x)=<br />
!<br />
n=<br />
1<br />
{ }<br />
nx<br />
n<br />
" 2<br />
At x = a<br />
2b<br />
, gcd ( a, 2b)= 1,<br />
<strong>the</strong> function jumps by<br />
! 2<br />
2<br />
8b<br />
The key to <strong>the</strong> integrability is that given any positive number,<br />
no matter how small, <strong>the</strong>re are only a finite number <strong>of</strong> places<br />
where is jump is larger than that number.