Prove $\ln (x)$ is continuous using $\epsilon-\delta$ Remark: Actually, $1-\frac {1} {e^ {\epsilon}}$ is the smaller of the two, so in effect we are letting that be $\delta$ But we really don't need to bother finding that out: all we need to do is to show there is a $\delta$ that works
real analysis - Does the epsilon-delta definition of limits truly . . . This quote resonates with my current dilemma Does the Epsilon-Delta definition truly capture the essence of what we mean by a 'limit'? though the epsilon-delta definition is a mathematical construct, what evidence do we have that it accurately reflects our intuitive concept of a limit?