Add new comment
Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
A game you're almost certain to lose...
What are the challenges of communicating from the frontiers of mathematical research, and why should we be doing it?
Celebrate Pi Day with the stars of our podcast, Maths on the move!
Maths meets politics as early career mathematicians present their work at the Houses of Parliament.
Celebrate this year's International Women's Day with some of the articles and podcasts we have produced with women mathematicians over the last year!
I'm sorry, but why did you substitute Z with zero? Where the hell did you get that? I think you forgot that the equation is not a function, and you can't substitute it with a value of zero, since we don't know the value of Z yet. You can't contradict a statement and substitute it with a value since the person is still trying to find the value. Also, 1-1+1-1+1... is Grandi's series, search it, and its been proven that the sum IS negative one, as proven by the diverging averages of the partial sums to one-half
(1/1), (1+0)/2, (1+0+1)/3, (1+0+1+0)/4, ... (1+0+1+0+1+0+1+0+1+0+1+0+1+0+1)/15, and so on. As you can see, it slowly alternates between other numbers and 1/2, but the difference between the alternates diverges to zero as the number of partial sums increase, thus, the equation does diverge to one-half.