Isabel Allende is a consummate storyteller. By her own admission, she tends to turn everything into a story — she even claims to have married her second husband in order to claim his life story for a ...
It is just what you want it to be, as long as it makes sense mathematically. We can talk about $+\infty$ and $-\infty$ in the extended real line, and about $\infty$ in the extended comlex plane. We can talk about cardinalities of sets, or about ordinals, too. The concept of "infinity", meaning "not finite" has very different and various meanings and uses in mathematics.
sequences and series - What is the sum of an infinite resistor ladder ...
I am a little confused about how a cyclic group can be infinite. To provide an example, look at $\langle 1\rangle$ under the binary operation of addition. You can never make any negative numbers with
This resolves your problem because it shows that $\frac {1} {\epsilon}$ will be positive infinity or infinite infinity depending on the sign of the original infinitesimal, while division by zero is still undefined. This viewpoint helps account for all indeterminate forms as well, such as $\frac {0} {0}$.
+1 that's a great answer. Especially for the last point: I agree that Zeno's paradox is basically an example of how there can be infinitely many intervals in a finite period of time. I didn't know that there was such a controversy on Zeno's intentions though; looking on wikipedia it seems clear that Zeno invented the paradoxes to support Parmedine's notion that motion is an illusion