Phew, I'm exhausted after just skimming that and I think I've a rough gist of it.
I suppose it's a rigorous modern-day answer to things I took for granted as not being that complicated. Zeno's paradoxes and the convergent series (1/2 + 1/4 +1/8…, etc.) never summing to 1 but in the limit they did. …And etc.
I'm reminded of the simple way to explain calculus to kids, that's the story of the frog on a rock in the middle of a pool who wishes to get to pool's edge and he does so by first jumping half way then a quarter and so on ad infinitum—and eventually he drowns as he never makes it to shore.
Kids are upset so teacher brings in Mr Calculus to the rescue. Fog actually makes it because his feet are too big.
Neat! It feels like bridging the gap between infinitesimals intuition and epsilon-delta formalism. I wonder whether this approach could make a 1st course more rigorous, and whether that would be a good thing.
Phew, I'm exhausted after just skimming that and I think I've a rough gist of it.
I suppose it's a rigorous modern-day answer to things I took for granted as not being that complicated. Zeno's paradoxes and the convergent series (1/2 + 1/4 +1/8…, etc.) never summing to 1 but in the limit they did. …And etc.
I'm reminded of the simple way to explain calculus to kids, that's the story of the frog on a rock in the middle of a pool who wishes to get to pool's edge and he does so by first jumping half way then a quarter and so on ad infinitum—and eventually he drowns as he never makes it to shore.
Kids are upset so teacher brings in Mr Calculus to the rescue. Fog actually makes it because his feet are too big.
Neat! It feels like bridging the gap between infinitesimals intuition and epsilon-delta formalism. I wonder whether this approach could make a 1st course more rigorous, and whether that would be a good thing.