On 29 Jan 2014, at 22:28, Russell Standish wrote:
As someone pointed out, it requires a non-standard definition of
convergence, as these series are non-convergent according to the usual
Cauchy definition.
IIRC, it may be Abel summation? I remember Abel summation being
mentioned during my
On 30 Jan 2014, at 00:07, LizR wrote:
On 30 January 2014 12:11, Russell Standish li...@hpcoders.com.au
wrote:
Yes. Pity the poor blighters at high school if someone tried to teach
them this stuff. I remember someone once showed me the definition of
continuity in year 11 (with all the upside
On 31 January 2014 04:43, Bruno Marchal marc...@ulb.ac.be wrote:
On 30 Jan 2014, at 00:07, LizR wrote:
On 30 January 2014 12:11, Russell Standish li...@hpcoders.com.au wrote:
Yes. Pity the poor blighters at high school if someone tried to teach
them this stuff. I remember someone once
OK... thanks, I should have guesses it was the zeta function :D
Anyway, I showed this proof to my 15 year old son and he soon put me right
on why 1-1+1-1+1-1+1... is indeed 1/2.
call the series 1-1+1-1+1... S
then 1-S = 1 - (1-1+1-1+1-1+1...) = 1-1+1-1+1-1... = S
S=1-S, so S=1/2 (which is, I
On Wed, Jan 29, 2014 at 9:56 PM, LizR lizj...@gmail.com wrote:
OK... thanks, I should have guesses it was the zeta function :D
Anyway, I showed this proof to my 15 year old son and he soon put me right
on why 1-1+1-1+1-1+1... is indeed 1/2.
call the series 1-1+1-1+1... S
then 1-S = 1 -
As someone pointed out, it requires a non-standard definition of
convergence, as these series are non-convergent according to the usual
Cauchy definition.
IIRC, it may be Abel summation? I remember Abel summation being
mentioned during my elementary analysis course, but nobody seemed to
That's basically how the guys in the video summed it.
On 30 January 2014 10:11, Telmo Menezes te...@telmomenezes.com wrote:
I've noticed something (maybe silly, maybe trivial?). Let's say:
S(0) = 1 = 1
S(1) = 1 - 1 = 0
S(2) = 1 - 1 + 1 = 1
S(3) = 1 - 1 +
On 30 January 2014 10:28, Russell Standish li...@hpcoders.com.au wrote:
As someone pointed out, it requires a non-standard definition of
convergence, as these series are non-convergent according to the usual
Cauchy definition.
Surely they are non convergent full stop?
But even so I can't
I just went upstairs and dug out my copy of Marsden's Elementary
Classical Analysis (don't you love the way advanced maths books are
elementary this, or elementary that - except for my favourite,
Mathematics Made Difficult, by Linderholm).
It's the concept of Cesaro 1-summability that I was dimly
On 30 January 2014 11:56, Russell Standish li...@hpcoders.com.au wrote:
I just went upstairs and dug out my copy of Marsden's Elementary
Classical Analysis (don't you love the way advanced maths books are
elementary this, or elementary that - except for my favourite,
Mathematics Made
On 30 January 2014 11:56, Russell Standish li...@hpcoders.com.au wrote:
It's the concept of Cesaro 1-summability that I was dimly recalling
(page 125), but on page 126, it appears the same result is achieved by
Abel summability, which is more general.
Is Abel the person after whom Abelian
On Thu, Jan 30, 2014 at 11:57:12AM +1300, LizR wrote:
On 30 January 2014 11:56, Russell Standish li...@hpcoders.com.au wrote:
It's the concept of Cesaro 1-summability that I was dimly recalling
(page 125), but on page 126, it appears the same result is achieved by
Abel summability,
On Thu, Jan 30, 2014 at 11:53:31AM +1300, LizR wrote:
If I ever write a book on the behaviour of birds native to the Antarctic, I
must call it Elementary penguin singing hare krishna
I might need an explanation of this. My cryptic crossword solver
moduler has just blown a fuse.
--
On 30 January 2014 12:11, Russell Standish li...@hpcoders.com.au wrote:
Yes. Pity the poor blighters at high school if someone tried to teach
them this stuff. I remember someone once showed me the definition of
continuity in year 11 (with all the upside down As and back to frount
Es), and it
On 30 January 2014 12:12, Russell Standish li...@hpcoders.com.au wrote:
On Thu, Jan 30, 2014 at 11:53:31AM +1300, LizR wrote:
If I ever write a book on the behaviour of birds native to the
Antarctic, I
must call it Elementary penguin singing hare krishna
I might need an explanation of
On Thu, Jan 30, 2014 at 12:07:08PM +1300, LizR wrote:
On 30 January 2014 12:11, Russell Standish li...@hpcoders.com.au wrote:
Yes. Pity the poor blighters at high school if someone tried to teach
them this stuff. I remember someone once showed me the definition of
continuity in year 11
On 30 January 2014 12:34, Russell Standish li...@hpcoders.com.au wrote:
On Thu, Jan 30, 2014 at 12:07:08PM +1300, LizR wrote:
On 30 January 2014 12:11, Russell Standish li...@hpcoders.com.au
wrote:
Yes. Pity the poor blighters at high school if someone tried to teach
them this stuff.
I think the problem is that for non-converging series, there are multiple
similar tricks you could do that would give different answers...for example:
S = 1-1+1-1+1-1...
-1*S = -1+1-1+1-1+1...
For a finite or converging series, the order of the summation doesn't
affect the final sum, so if in
On Wed, Jan 29, 2014 at 6:39 PM, LizR lizj...@gmail.com wrote:
On 30 January 2014 12:34, Russell Standish li...@hpcoders.com.au wrote:
On Thu, Jan 30, 2014 at 12:07:08PM +1300, LizR wrote:
On 30 January 2014 12:11, Russell Standish li...@hpcoders.com.au
wrote:
Yes. Pity the poor
On 30 January 2014 12:45, Jesse Mazer laserma...@gmail.com wrote:
I think the problem is that for non-converging series, there are multiple
similar tricks you could do that would give different answers...for example:
S = 1-1+1-1+1-1...
-1*S = -1+1-1+1-1+1...
For a finite or converging
On 30 January 2014 12:48, Jesse Mazer laserma...@gmail.com wrote:
On Wed, Jan 29, 2014 at 6:39 PM, LizR lizj...@gmail.com wrote:
On 30 January 2014 12:34, Russell Standish li...@hpcoders.com.au wrote:
On Thu, Jan 30, 2014 at 12:07:08PM +1300, LizR wrote:
On 30 January 2014 12:11, Russell
On 18 Jan 2014, at 02:27, LizR wrote:
The demonstration that the sum of the positive integers is -1/12
relies on the assumption that the sum of
1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 -
1 is 1/2
However that is by no means certain.
It is 1 - 1 + 1 - 1 +
It was that wonderful Indian mathematician Srinivasa Ramanujan who first
came up with the proof in 1913.
https://en.wikipedia.org/wiki/Ramanujan_summation
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Alberto,
What is amusing is that Ramanujan said this (that 1+2+3+... = -1/12)
in a letter to find a job in England, just to illustrate that he was
not bad in computing. He was of course considered as crackpot until
the letter was given to Hardy, who recognized immediately the genius.
Amazing.
That means that there are much left to discover in math.
And also note that:
1/12 = 2/24 and 24= flip 42 for some well known flip : N - N
;)
2014/1/18, Bruno Marchal marc...@ulb.ac.be:
Alberto,
What is amusing is that Ramanujan said this (that 1+2+3+... = -1/12)
in a letter to
That is absolutely wrong. Everyone know that the result is 42 ;)
2014/1/17, Craig Weinberg whatsons...@gmail.com:
http://sploid.gizmodo.com/the-sum-of-1-2-3-4-5-until-infinity-is-so-1503066071
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http://en.wikipedia.org/wiki/Deep_Thought_(The_Hitchhiker%27s_Guide_to_the_Galaxy)#Deep_Thought
2014/1/17, Alberto G. Corona agocor...@gmail.com:
That is absolutely wrong. Everyone know that the result is 42 ;)
2014/1/17, Craig Weinberg whatsons...@gmail.com:
Adams wasn't the only one to figure it out...
http://www.amazon.com/Prayer-Kabbalist-42-Letter-Name-God/dp/1571895752
:)
I forget how many times you have to say DEMOGORGON before he is summoned.
On Friday, January 17, 2014 12:45:22 PM UTC-5, Alberto G.Corona wrote:
Google can not lie you:
https://www.google.es/search?q=the+answer+to+life%2C+universe+and+everythingoq=the+answer+to+life%2C+universe+and+everythingaqs=chrome..69i57j0l5.402j0j9sourceid=chromeespv=210es_sm=93ie=UTF-8#q=answer+to+life+the+universe+and+everything
2014/1/17, Craig Weinberg
The demonstration that the sum of the positive integers is -1/12 relies on
the assumption that the sum of
1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 is
1/2
However that is by no means certain. The sum could be undefined, in which
case the proof simply fails. Or it
That's pretty much what I thought. The idea that the sum of such a series
*equals* 1/2 I think is only one way to make sense of it. Who says that a
rational number is even an option? What if +1 and -1 are absolute, like
'moving' and 'static'. There is no 1/2 moving. Still, it's interesting to
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