The continuous and the discrete.

The first "graph" is a function f having a positive derivative at 0, but not increasing in any neighbourhood of 0.


The second "graph" shows that there is no knight's tour on a 4-by-4 chessboard.  
(In case you were wondering, a formula for f is: f(0)=0, 
f
(x)=x2sin (1/x) +x/2 if x=0.)
 











 

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