Merychris Calib-og said...
How can I find the following cardinalities?
Sunday, January 31, 2016 at 7:29 AM
The term above -143n^10 should be -143n^10/60. Inadvertently the denominator 60 was omitted.Also the term n^c should be +n^c with
a plus sign inserted. Integrating this corrected function from 0 to -1
will now render the result of -1/12 = RZ(-13) = RZ(-1). Alan Walter,Sydney.
Friday, January 29, 2016 at 9:00 PM
Thanks for your youtube email reference.
RZ(-c) is Riemann's Zeta value at -c = I(n=0to -1)[1^c+2^c+3^c+...+n^c]dn
Where I(n=0to-1) is the definite integral from 0 to -1(lower limit)
RZ(-13)=I(n=0to-1)[1^13 +2^13 +3^13 +...+n^13]dn
+715n^4/132 -691n^2/420]dn= -1/12 on evaluation= -B(14)/14= -(7/6)(1/14)
Note1^c+2^c+3^c+...n^c for odd c values has factors of n(n+1)with zeros at 0,-1.
Anyone interested in an expression for the yet unsolved sum of the positive ODD
Zeta series Z(2n+1) in terms of π^(2n+1)? Alan Walter, Sydney.
Wednesday, January 27, 2016 at 8:39 PM
The author of this article is absolutely correct to point out that these supposedly mysterious values can be found by calculating the definite integral between 0 and -1 of the expression for the respective sum to the nth term (a.k.a. their partial sum expressions).
This is also mentioned in this interesting 'response' video (it responds to the claims made in the video that is the subject of this discussion): https://www.youtube.com/watch?v=BpfY8m2VLtc
It shows what happens if you do the series manipulations with rigorously (hint - you do not get -1/12) and it explains why other methods get this -1/12 result.
The response video claims this -1/12 result is the result of a mistake. The mistake is one of taking a function that applies to just positive whole numbers, manipulating it in ways that bring decimal numbers and negative numbers into play, and then interpreting the result as though it still relates to positive whole numbers.
Tuesday, January 26, 2016 at 7:02 PM
Dr Ebute said...
Contact Dr Ebute, for any kind of problem...
HIV/AID,CANCER,LOVE SPELL,GOOD JOB,PROMOTION,ETC...
I wish i have found this spell caster earlier before spending my money on
spell without result.His powers are really amazing and i enjoyed the
satisfaction i gained from using his spell. He is really gifted with powers
to help people with their various problems. His email is
firstname.lastname@example.org called him on his phone number +2348071145063
Thursday, June 4, 2015 at 12:24 AM
Let's assume I gave you zero fucks. How many fucks have I given you?
Friday, May 15, 2015 at 11:28 PM
Interesting, except removing thingZ from bagA doesn't leave you with -thingZ in bagA. to do that you would have to remove 2*thingZ. Otherwise, taking thingZ out of bagA, and then replacing it would leave you with nothing in bagA. But clearly removing thingZ from bagA and replacing it shouldn't make thingZ dissappear.
Friday, April 3, 2015 at 9:39 AM
I understand how puzzling it can be. Is zero a quantity or not? Is a negative number a quantity or not? Talking about apples and pears is a little worn out, I think.
There are two different bags; let's call them bagA and bagB. They are freshly made, and nothing has ever been put in them before.
Each bag has nothing in it. The bags are in an enclosed vacuum, so there is no air in them and no air outside of them.
There are two different things; let's call them thingZ and thingY.
You put thingZ into bagA, and thingY into bagB.
You then have a bag - bagA - containing thingZ and a bag - bagB - containing thingY.
If you remove thingZ from bagA and thingY from bagB, the bags will then be empty because the things that were in them have been removed.
Because there used to be a thingZ in bagA, and one was taken out, there is a shortage of one thingZ.
BagA therefore contains -1 thingZ.
Likewise, bagB therefore contains -1 thingY.
But all the time there was a thingZ in bagA, bagA also had no thingY.
Similarly, while there was a thingY in bagB, bagB also had no thingZ.
In fact, ever since the bags were made, there was also none of thingX, none of thingW, no tomatoes, onions, apples, bicycles, orang-utans or saxophones in them. None of any other thing, in fact, in either bag. And the same goes for what is outside of each bag either, because it was a vacuum.
If it is true that zero is something that does exist, then zero is a complete lack of stuff. But we know that it wasn't always like that, because there used to be a thingZ and thingY in the bags.
Regarding anything and everything else, there always was a complete lack of anything else in the bags, and everything outside the bags.
Because you cannot remove something that isn't there, bagA still contains zero thingY and bagB still contains zero thingZ - and zero everything else except as was stated in the paragraph before this one. And outside of the bags is still zero everything.
But the bags don't contain zero of everything, they contain -1 of one thing.
Zero is more than -1. The bags therefore collapse under the pressure of absolutely nothing.
Friday, April 3, 2015 at 2:30 AM
do you wants....idea from amateur...from me or not...
Easy...! Open Mind...
Zeta Functions not importtant ....Harmonic important more!
Zeta function that important Zeta(-1) and Zeta(-3)
I show you....develop zeta in term cartoon.....and blinding set and anti
and i predict somethings in Higher Dimension...You can help me proof
Wednesday, December 3, 2014 at 11:13 PM
To be more specific, irrational mathematics('mathematics'), is not sustainable.
Monday, November 3, 2014 at 11:53 PM
I have posted a message explaining the dilemma.
What has happened here was inevitable, mathematics is not sustainable.
Here is the link to my message: http://marques.co.za/duke/news_win.htm
It will not surprise me if this comment is censored (Moderated)
Friday, October 31, 2014 at 5:13 AM
1+2+3+4+... = -1/12 (R) where (R) is the Rumanujan Summation. This is not a normal -1/12. It basically is a categorization of the series in question. It should be read, "the sum of one plus two plus . . . has a Rumanujan summantion of -1/12" (as opposed to "equals -1/12").
Tuesday, October 14, 2014 at 3:12 PM
Johnson Briney said...
Contact a Great man on email@example.com or call him on +2347060552255 who help me to solve my problems when my ex boyfriend was blackmailing me after trying many ways to stop him but it didn't work for me until i met this man who help me cast a spell that stop him for blackmailing me and now he is pleading forgiveness and i believe he can solve any problems you are having because he just solve mine.
Sunday, August 31, 2014 at 9:38 AM
way2 college said...
Valuable liveliness is also saved which you can set aside to your family or to manually. Completing an Online Distance Learning course gives you more flexibility while studying over conformist classroom set up.
Saturday, August 9, 2014 at 1:31 AM
No, zero is not in the real world.
Imagine that you have two bags, in one there is one apple and in the other you have one pear. Then we remove the apple and the pear out of the bags, now in one bag you have zero apples and in the other zero pears, but zero apples and zero pears have the very same properties, therefore they must be the same thing, as we know, pears and apples are not equal to each other, so it must be that zero is nothing but a concept that does not exist in the real world.
Monday, June 2, 2014 at 1:58 AM
Area A = Area B since they both are infinitely large areas. That series diverges, you learned that in Cal2 or Math Physics of DiffEq. C'mon.
Thursday, May 29, 2014 at 10:47 AM
Richard Smart said...
This article is superb, I love it. That infinite series thing really perturbed me when I first saw it but I couldn't see how to examine it more effectively such that I could get to the point that I wasn't perturbed by it any more. Watching you do it above now makes me annoyed I didn't have the idea of doing that myself. But the fact is I didn't. So simple, so insightful, so satisfying. Thanks for that and if you could now just solve every other annoying problem for me I would be most grateful ;o)
Thursday, May 22, 2014 at 3:41 PM
Bernd Jantzen said...
Of course, the partial sums of 1+2+3+4+... are tending to infinity. Nobody claimed anything different. The whole discussion here is about how to assign a meaningful finite value even to a divergent sum like this one. And the discussion is about the question whether one may call this finite number the value of the divergent series or just a meaningful number that one may use in replacement of the series under some conditions.
Sunday, April 6, 2014 at 6:01 PM
Saturday, April 5, 2014 at 10:22 AM
Saturday, April 5, 2014 at 10:20 AM
i think 1+2+3+4+.........=infinity
Saturday, April 5, 2014 at 10:18 AM
I possess no sheep, therefore I possess 0 sheep. 0 is very much in the real world.
Wednesday, March 19, 2014 at 11:08 AM
Imre Fabian said...
For me, not a mathematician, this is a perfect example for that you can prove anything with infinity mathematics.
In my view, infinity does not exist (in the real world), nor does 0.
Infinity = anything / 0
0 = anything / infinity.
Physical argument: the smallest thing (measure) is the planck dimension (planck lenght, planck time etc.) so there cannot be an infinite number of since the beginning of time (the big bang).
Wednesday, March 5, 2014 at 4:58 AM
Cre Master said...
It takes a brave man to admit when he has got something wrong but to be now admitting your 'wrongness' is not as wrong as first thought must have been a mission, so well done.
However could I bother you for a small clarification? When you said "And of course, the difference between area A an B is itself infinity if you extend the curves out infinitely." I assume that you are not taking about the area of region A compared to the area of region B since aren't these exactly the same?
Saturday, February 8, 2014 at 10:47 PM
Bernd Jantzen said...
Hey Buzz, it's a pity that you have now reverted to your previous viewpoint instead of accepting that 1+2+3+4+... simply is not equal to -1/12 (although the two are related to each other).
So you are now claiming: "I still believe 1+2+3+4+ . . .= -1/12, if the ENTIRE infinity of whole numbers are included" (cited from your updates of Feb 6th above).
But what do you actually mean by "1+2+3+4+... with the entire infinity of whole numbers included"? No mathematical definition exists of what your statement should mean.
You obviously don't mean adding consecutively more and more of these numbers, because this standard definition of the value of an infinite sum diverges here and does not yield a finite number.
Do you mean "1+2+3+4+..." understood in the sense of Ramanujan summation or zeta-function regularization? Then the result is indeed -1/12. But neither Ramanujan summation nor zeta-function regularization actually yield the sum of infinitely many terms of a divergent series. They are simply procedures to treat divergent sums and assign them finite values in a consistent and meaningful way. Both of these procedures actually use analytic regularization to drop in a well-defined way the divergent and infinitely positive contribution originating from the upper end of the summation. So that's how both procedures find the negative result -1/12 from what originally was a sum of purely positive numbers. But, when you look at how Ramanujan summation or zeta-function regularization obtain this result, you may convince yourself that this result is not equal to the sum of the infinitely many numbers of the original series, but that it follows from this series in a more complex and intricate way.
Simply stating "1+2+3+4+... with the entire infinity of whole numbers included" does not mean anything in mathematics. It only means something if you already have a certain regularization procedure in the back of your mind.
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.
Saturday, February 8, 2014 at 5:03 PM