[Cauchy convergence test is proven wrong] - A New Kind of Science: The NKS Forum

Pages:1

# Cauchy convergence test is proven wrong

Posted by: damsell

The australian philosopher colin leslie dean proves Cauchy convergence test
is wrong
and maths as a consequence ends in meaninglessness

.333333[BAR] is shown to converge to 1/3
but 1/3= .33333[BAR]
so if they are the same number then there has been no convergence
but Cauchy convergence test says .3333]BAR] convergence

either 1/3 =/ .33333[BAR] AND IS A DIFFERENT NUMBER THAN .33333[BAR]

or
Cauchy convergence test is proven wrong
both ways we have a contradiction
again evidence for colin leslie deans claim that maths ends in
meaninglessnes

Posted by: Jason Cawley

"if they are the same number then there has been no convergence"

They are, and why would there need to be?

.3
.33
.333

are all different numbers, and converge to 1/3.

1/3 doesn't converge to 1/3, it is 1/3.

Naturally there are an infinite number of simple arithmetical operations that equal any given number. 4 is 5 minus 1 or 6 minus 2 etc. There can never be uniqueness at that level.

Posted by: damsell

if they are the same number then there has been no convergence"

They are, and why would there need to be?

if 1/3=.3333[R]
and .333[R] converges to 1/3
then all you are saying is .3333[R] converges to .3333[R]
AND THAT IS NO CONVERGENCE
thus cauchy convergence test is eith wrong
or
1/3 is a different number to .3333[R]

either way there is a contradiction and as dean says maths end in meaninglessness

Posted by: damsell

support that 1/3=/.3333[R]
FROM SIC LOGIC

you say 1/3 + 1/3 +1/3 = 1
> but
>
> 33333... + .33333... + .33333... = .9999...
> not as you say .9999... = 1
> as dean has shown
> 9999...=/1
>
> another proof 1/3 =/ .3333...
> 3333... is shown to converge to 1/3
> thus 1/3 must be a different number from .33333..
> but you say 1/3 = .3333..
> thus they are the same number
> but that means there has been no convergence
> but this contradicts the cauchy convergence test

All right, since 1/3 != .333...., what is it equal to?
(This does solve the rational closure problem, though.)