Dear SteeleRedux,

Sorry, but that quote does not make much sense to me.

I can only repeat: You do not need any integration or Wolfram to see that the regions A and B are MIRROR IMAGES of each other (with respect to the parabola’s vertical axis), and BECAUSE OF THAT (nothing to do with “subtracting” infinities) both have the same (infinite) area.

I do not see where 1+2+3+4+... comes into it, except that if f(x)=x(x+1)/2 is the function whose graph is that parabola, then f(n) = 1+2+3+ ... +n. i.e. it is a partial sum of the infinite series 1+2+3+4+ ... . Thus if A(x) is the area of the region under the parabola above the segment [0,x] (for x>0), then its RATE of increase - i.e. the derivative dA(x)/dx which is f(x) - tends to infinity as fast as 1+2+3+4 ... . That is all that I can see about relating A (or B) to 1+2+3+ 4 + ... .

Dear George,

Many thanks for the effort you have put in on this thread and to the others who have contributed. As I no have only one nostril above the surface I think I had better call it quits. I'm off to study a little more math, and to practice a couple of neat card tricks the Numberphile crew have shown on their Youtube channel. Doing base 3 calculations in a few seconds is still not quite in my comfortable grasp but I think it is worth it. Impressed me.
http://www.youtube.com/watch?v=l7lP9y7Bb5g

Cheers mate.

Dear Warmair,

I thought you might be interested in a little update to the link you provided. Buzz has corrected his correction, at least to a degree, and Bernd has left in disgust.

“Anyway, I have the impression that further debates here are useless. You probably cannot understand what I have tried to explain through my many comments. So I will stop wasting my time any longer.”

And I'm left like a shag on a rock.

Still it looks like the debate will continue for some time yet.

Is there no end to this.

JAYB..infinity cannot bE 1/12th

why?

<<..[ITS..mathematical shorthand

for.."minus infinity
*is less than any real number,..

and *infinity is greater than any real number"

1/12 TH..IS LESS THAN ANY REAL finite..NUMBER..
Further...AS INFINITE..ISNT even..A NUMBER..[let alone a MINUS NUMBER.

BUT IF IT WAS IT WOULD BE A WHoLE NUMBER/
IT MUST BE GREATER..[or if negative lesser]..than any whole number

BUT..ITS not..a NUMBER
..1/12..IS A FRACTION..OF A WHOLE NUMBER

ie..[ITS ALL JUST NON*SENSE]
WALK AWAY..I have..some people with nuthin..want it all

BUT IF IT.s ALL..=..1/12..TH..is insane.
LIKE CALLING...EVOLUTION/A SCIENCE..when its a theory...WITH NO Falsifiable..[NO abILITY TO REplicate..TO CONFIRM..IT..

CAN 1/12 TH-INFINITY
OF COURSE NOT..case closed

Didn't get it, did he.