4 ms·
Reminds me of the paradoxes of Zeno [1], especially the paradox of Achilles and the tortoise. At least one can simply prove that 0.999... = 1 without much hard
by smlckz 6y ago
Reminds me of the paradoxes of Zeno [1], especially the paradox of Achilles and the tortoise.
At least one can simply prove that 0.999... = 1 without much hard work. Maybe less controversial than the following:
1 + 2 + 3 + ... [somehow] = -1/12 {{Riemann's zeta(-1)?}}
1 + 2 + 4 + 8 + 16 + ... [somehow] = -1
As well as the weird prime product (Product of 1/(1-(p^-2)) for p prime) and the sum of x^-2 from x=1 to [sigh] being equal to (pi^2)/6 are some example of infinite beauty of mathematics that I remember.
[1]: https://en.wikipedia.org/wiki/Zeno's_paradoxes https://en.wikipedia.org/wiki/Zeno's_paradoxes
- cochne 6y agoIt's less controversial than those because it's actually true. The latter statements are not true with the traditional definition of a sum.
- gilbetron 6y ago1 + 2 + 3 + ... does not equal -1/12, except if you redefine what you mean by +. https://www.youtube.com/watch?v=YuIIjLr6vUA https://www.youtube.com/watch?v=YuIIjLr6vUA
- frogpelt 6y agoYour two examples can be debunked though. See here: https://www.youtube.com/watch?v=YuIIjLr6vUA https://www.youtube.com/watch?v=YuIIjLr6vUA
- smlckz 6y agoah, Mathologer video. Have seen that. Another one by 3b1b on that topic: https://youtube.com/watch?v=sD0NjbwqlYw https://youtube.com/watch?v=sD0NjbwqlYw