Confused

[Neal]

I have looked at J. Noel Cooks paper and find it rather absurd.
It assumes there IS a value to 1/0 and seems to use explicit values
of x to prove an equation valid for all x.

And as a result gets explicitly wrong answers.

For example, at random

Equation 50 states
(-pi i)/log(x+1) = x^1/2

re-arranging this gives
(-pi i)=log(x+1).x^1/2
exponentiate both sides

e^(-pi i)=(x+1)^(x^1/2)

now e^(-pi i)=1/e^(pi i)=1/-1=-1
so we have
(x+1)^(root(x))=-1 for all x

hmm. try x=1 (as per the proof of this equation) and you get
(1+1)^(1^1/2)=2 ^1 or 2^(-1). so either 2 or 1/2 =1.....Not true

The basic premise that one can start with an undefineable value such
as 1/0 and conclude anything is false

e.g. Assume there is some number k=1/0

then k=1/(a-a) for all a
invert both sides (valid if k exists and is not 0)
1/k=(a-a)
multiply by k both sides
1=k(a-a)
1=ka-ka
so 1=0
Proof by contradiction. There is no k=1/0

[he...@jeffreyncook.com]

Neal,

There is a typo in eq. 50, where I left out the ‘y’ in the numerator.
However, it is referred to directly below the equation.
Your comment:

“so we have (x+1)^(root(x))=-1 for all x”

Might I suggest you read the sentence right above eq.50, particularly
the point “when x = 1”. And the last sentence in that section,
particularly, “negative counterparts with some error term…” So what
you have done above is obviously not correct, nor what I have stated.

I will add the y, as this variable is included in the Definitive
Theorem and it is referenced.

For the other part of your comment, might I suggest you read this
page:

http://www.singularics.com/science/mathematics/discussion/series1/


Thanks,

Jeff