What is the sum of all natural numbers? That is 1 + 2 + 3 + 4 + 5 + 6 + … ∞
Spoiler
minus 1/12 See proof here.
I also had trouble accepting that 1 + 1 – 1 + 1 – 1 + 1 … ∞ = ½ until I accepted infinity as a concept, not a number. The series must be allowed to go on forever.StuartR wrote:That's ridiculous. I'm not convinced by the assertion that 1-1+1-1+1... = 1/2, I would have said that series does not tend towards a limit as the number of terms increases, so you can't give it a value.
Oh Hans; you do seem to have dropped the cat amongst the pigeons. I cannot find a flaw in your argument, though I am still looking.HansV wrote:By the way, using the same method, I can prove that 0 = 1:
And oddly enough, many physicists don't attach much weight to string theory because it's "only" a mathematical theory... not a scientific theory.HansV wrote:That's why mathematicians have trouble taking physicists seriously...