A Couple Videos

A long time ago, minute physics posted these excellent videos (yes, the "proof" in the first doesn't really work, but yes, that series can be said to converge to -1):

Recently, someone posted this response:

This third video isn't mathematically correct--though there is some really really interesting mathematics in it. Our initial reaction is, I believe, to tell the author of the third video that he's just wrong. But I don't think that's the right approach--indeed, I think he's doing something we all should do more of, thinking about math. Yes, his argument doesn't quite work. But, he's reasoning about math. He's found something that doesn't make sense to him--that sounds wrong to him--and he's grappling with it, trying to show it's wrong. And he's found something substantive, not something trivial, like in so many math facebook memes. (What's 1+1+1+1+1+1x0+1= ? Does anyone really care?) Isn't this what we would want people to do, in any other subject--to make arguments, and thereby, to learn?