Wow, if Phil Plait fell for that nonsense I guess we can forgive Singularity for being taken by it. But... no, that's just dumb. Like, it should be immediately obvious to anyone with any proficiency with math *at all* that it doesn't make sense.

Meh. I haven't responded to his posts since he's yet to actually challenge any point I've made. Of course, if he wants to disprove the standard equation written in textbooks across the world and all the string theorists who depends on that axiomatic identity, he can't just give it away for free on the internet.

Also, that informal proof on numberphile is non-rigorous, but does help illustrate the problem in widely accessible terms.

By the way, I did like the thought experiment: If "+1 -1" equated to turning the lights on and off, and if each new number in the series happened over shorter and shorter time approaching an asymptote in time, than once the time is passed, you've "switched the lights an infinite number of times". Had we stopped at any point along the way, we could have determined if we were on an even or odd count. But after the minute is up, would the lights be on or off? Or in some waveform/indeterminate state expressing both binary states?

Honestly I thought the source of discussion would be defining what it means to be considered "equal", which is highly semantic. Considering its superior power modeling our universe, I've argued it can and should be considered "equal" under a branch of math that uses analytic continuation. It surprised me to see him straight up argue that result is trash to the same extent that 1 = 3 would be trash. :\