>They add up all positive intergers from one to infinity. What do you think the sum would be? Infinity? Nope. The sum is actually -1/12.Things aren't this simple when you're working with infinities. You can't just shift things around like this and still get meaningful results.
Consider this sequence:
And try:
| N - N | = | 1+ 1 + 1 + 1 + 1 ... | |
| | | - [ 1 + 1 + 1 + 1 ... | (shifted slightly, like they did in the video) |
|
|
| |
| N - N | = | 1+ 0 + 0 + 0 + 0 ... | |
| 0 | = | 1 | |
It's as easy as that to show a contradiction when you assume that normal rules of addition can apply to infinite sets. In reality, you need to expand the definition of addition to apply it to infinite sets, which is usually done via the concept of limits.
- Greminty
