I will add to the comments nearby and say that I found that video appalling. They write
S = 1 - 1 + 1 - 1 + ... = 1/2,
and justify this nonsense statement with some hand-waving, and then proceed to use this "fact" to deduce several other "facts" through manipulation of infinite sums. (Sure, the statement is true under some interpretations of "...", "+", and "=", but they never tell the viewer that they are using a particular, and non-standard, interpretation.)
Then, at the end, they really ice the cake by appealing to "physics" and "string theory" to affirm that it is all true.
It's mystical, and abuses the appeal to authority. It's the reverse of what math should be.
Additionally, for someone who suffered through real analysis, it's galling to have an issue that legitimately confused mathematical geniuses in the 1800s (convergence and the nature of the "passage to the limit"), and was then figured out, used to troll people in the 2000s.
Phil Plait ("Bad Astronomer") used this in his column, and the results were disastrous. This is the only time I've seen him make such a bad mistake, he's usually both fun and correct.
Then, at the end, they really ice the cake by appealing to "physics" and "string theory" to affirm that it is all true.
It's mystical, and abuses the appeal to authority. It's the reverse of what math should be.
Additionally, for someone who suffered through real analysis, it's galling to have an issue that legitimately confused mathematical geniuses in the 1800s (convergence and the nature of the "passage to the limit"), and was then figured out, used to troll people in the 2000s.
Phil Plait ("Bad Astronomer") used this in his column, and the results were disastrous. This is the only time I've seen him make such a bad mistake, he's usually both fun and correct.