Add new comment
-
Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
Teo tells us about his work in artificial intelligence, his travels around the world, and how inspiration sometimes strikes in the pub.
Clouds make the weather, yet their detail isn't taken into account in weather forecasts. Artificial intelligence might be able to help.
Predicting the weather is hard. With more data and computing power becoming available, artificial intelligence can help.
How does your phone know what the weather's going to be like?
How a little insect can cause chaos.
If Z(-1) = 1+2+3+4+5+....= -1/12. & Z(0) = 1/1^0 +1/2^0 +1/3^0 +1/4^0 +...
Z(0) = 1+1+1+1+1+...
[Z(-1) +Z(0)] = 2+3+4+5+... = 1+2+3+4+5+... -1= -1/12 -1 = -13/12
This implies Z(0) = -1
[Z(-1) - Z(0)] = 0 + (1+2+3+4+5...) = -1/12
This implies Z(0) = 0
Both these values for Z(0) of -1 & 0 are contradictory.
Adding [Z(-1) + Z(0)] + [Z(-1) - Z(0)] = -13/12 -1/2 = -14/12 = -7/6
This implies 2Z(-1) = -7/6 => Z(-1) = -7/12This contradicts Z(-1) = -1/12 which
was the original assumption.
Putting infinite divergent series equal to a finite number appears to lead to
results that are not sensible.