Example of a (dis)continuous function The following thought came to my mind: Given we have a function $f$, and for arbitrary $\varepsilon>0$, $f(a+\varepsilon)= 100\,000$ while $f(a) = 1$. Why is or isn't this function continuous?
I thought that with the epsilon-delta definition, where we would chose delta just bigger then $100 000$, the function could be shown to be continuous. Am I wrong?

Hint:
Choose $0<r<10000-1$ 
Then $\forall~\epsilon>0,~|f(a+\epsilon)-f(a)|=10000-1>r.$
