Paradoxes

Thoughts on Zeno's paradox, as I understand it:
1. An infinite geometric series can converge to a definite number, therefore an infinite number of tasks can take a finite amount of time. 
2. An infinitely small segment is not an actual thing. Limits can be used to discuss what happens as the number lengths approaches infinity (the length approaches 0), but you can not say what happens at infinity. 
In short, plurality does not lead to contradiction. 

Thoughts on the Pensioner's Dilemma:
You might be tempted by possibly: confessions minimizes risk. But remember, they will reach the same rational conclusion; their decision is not arbitrary. And, whatever way you come to your conclusion, if you both arrive at "I should confess," you would both realize this is irrational: why both confess when you can both not confess?
If you assume the other prisoner will arrive at the same conclusion as you (since the most rational decision would be the most rational no matter how many times it is repeated), you would not confess. But the other man knows this, so you should confess and take advantage of him. But he should realize this too... So the question is who will extrapolate further and who will stop at the right point.