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1 + 1 [ 1
In the name of Allah.

I wish to apologise to reader about not writing in Arabic as I have no means to do so.

I was interested in the article, which contained abstract arguments concerning complex numbers and infinity, so I sought to put my thoughts in writing.

To say that infinity, : = x is to introduce 2 different arguments both of which prove that,

x + x ! 2x , 3x, or any other than :

1) If infinity = x, then x is undefined and it follows that it is not subject to mathematical assumptions and operations, and although not a singularity it exhibits some of its properties.

Therefore to say, x + x = 2x,

is like saying, x + y = 2x, 2y or 2xy. All of which would violates basic mathematics.

The argument should be expressed as,

x + y = :

This holds true with either or both variables are :. If either or both variables change then the problem becomes one of dynamics, i.e. changes with time and the variables would require redefinition with each new value. A solution can be found, but life is too short!

2) If infinity = x, and x belongs to a defined set or a known group, then to say,

x + x = 2x,

is a gross misrepresentation of the initial assumption that infinity includes all constants beyond a specific set deemed practical to justify an argument. Here, the addition of any constant to x can only lead to redefinition of x as being a larger infinity.

It therefore follows that x + x = x

Which agrees with true logic that

1 + 1 = 1, albeit : is always < 1

Therefore 1 + 1 [ 1,

And, x + x ! 2x

QED

Regards,

X, but not an infinite one.
x_2005@hotmail.co.uk

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