Re: Han's startling new set theory.


"Han de Bruijn" <Han.deBruijn@xxxxxxxxxxxxxx> wrote in message
news:c9273$4312ce26$82a1e3ad$31631@xxxxxxxxxxxxxxxxxxx
| cbrown@xxxxxxxxxxxxxxxxx wrote:
|
| > Han de Bruijn wrote:
| >
| >> 1/7 =
0.14285714285714285714285714285714285714285714285714285714285
| >>sqrt(2) =
1.41421356237309504880168872420969807856967187537694807317668
| >>
| > A few years ago, an error was found in the floating point section of
| > the Pentium processor, which caused it to give incorrect results to
| > certain functions:
| >
| > http://www.cs.earlham.edu/~dusko/cs63/fdiv.html
| >
| > How do you know that your calculations above are correct (i.e., that
| > whatever computer you perform them on is actually correctly
modelling
| > the conclusions which come from the axioms of arithemtic)?
|
| Use (two) different computers. If they both give you the same answer,
| then it's highly unlikely that such would be a coincidence. Don't you
| know how to carry out reliable physical experiments? Always duplicate
| in the first place.
|
| Han de Bruijn

sqrt(2) = 1 +0.414...
= 1+ 1/2.414...
= 1+ 1/ (2+ 1/2.414...)
= 1 + 1/(2 + 1/(2+1/(2+1/(2+1/(2...)))))

It is called an extended fraction, you can solve it to any desired
accuracy.
Androcles.


.

Relevant Pages

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