2 ms·
Sure. And it's true, 0.99... is equal to 1. All I'm saying is [SOPI below] it's all a little more technical than the junior high school proof. For example if
by tom-thistime 6y ago
Sure. And it's true, 0.99... is equal to 1.
All I'm saying is [SOPI below] it's all a little more technical than the junior high school proof. For example if 23+6\epsilon = 23, then how do I define 23 + 6\epsilon - 23? I can choose different approaches here, but "zero" is going to be pretty inconvenient when I go to do an integral.
[SOPI] Statement of Personal Ignorance. I don't quite know what I'm talking about. If you do know, please step in and help correct me.
- zests 6y agoWhat are you integrating over?
- tom-thistime 6y agoI'm taking the limit of any convergent infinite sum of terms each weighted by \epsilon. Although \epsilon itself equals zero, of course the limit of the sum isn't necessarily zero. So if we go and define some other funky "infinitesimal" \epsilon != 0 in the surreals, we have to be careful. Apparently people have done that kind of thing successfully, but it took a long time after Cauchy for that to happen.