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Old 2005-05-05, 17:18   #6
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Jan 2004

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Default Fermat's theorem

Thank you Crook for investigating the mystery of the infinite series.
As a result I have been able to go further in this investigation. However I must restrict this post by giving just one more rendition.

In the 19th century Bernard Bolzano was the first to treat this problem on a sound and logical manner. Since Zeno's paradoxes had put mathem'cians in a flummux there was a lot of speculation as to how to relate to infinity. Then Bolzano came along and treated the problem on a war footing.

Consider the series S = a -a + a -a +a -a +..............
If we group the terms thus we get
S = (a-a) +(a-a) .........
= 0

On the other hand we group the terms in a 2nd. way
We can write S =a -(a-a) -(a-a) -(a-a).........

Again by still another grouping
S =a -(a-a+a-a +a-a.............
S =a- S
Hence 2S=a or S=a/2 (so the learned proffessor/priest of Pisa Guido Grandi mentioned in an earlier post was not so wrong after all)

Today with maths on a firmer footing we can label it as a class of oscillating series between the values of 0 and a

Even more startling are the results obtained from the series in the special case when a = 1
I will reserve this for another post.

For further reading;
'Riddles in maths' by Eugene Northrop 1960
'The Paradoxes of the Infinite' by Bernard Bolzano1851 .

Last fiddled with by mfgoode on 2005-05-05 at 17:26 Reason: typo error
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