Re: infinity

Dear Tony:

Although I wasn't here at the beginning of the discussion but I have a
point of view and I don't know if it helps the discussion or not.

I think it is better to define the operation you are deriving finites
by, and also you should define what do you mean by the infinite trail.

For example lets take the simplest of finite numbers , the natural
numbers

and say that 0 is finite and +1 means "sucessor of " so 0+1=1 , and say
that the successor of a finite number is also a finite number ( Peano)

Define the infinite as the horizontal positioning of n+1 after n along
one line in the same direction like below:

N=0,1,2,3,4,...............

Now it is obvious that their is a natural finite number that is greater
in value than the value of any natural finite number in N above.

Proof:

Construct Q such that for every number is N their are two natural
numbers in Q , the infintie succession of natural numbers in Q is
defined below:
1357......
0246...... = Q

It is obvious that Q contains double the amount of natural numbers
contained in N, more specifically their are w of natural numbers in Q
not contained in N, so if we denote Q1 as the first w of natural
numbers present in Q ( which are the same as those in N) and Q2 as the
second w of natural numbers present in Q, then.

min Q2 = lim N.

and of coarse min Q2 is a finite natural number.

Of coarse min Q2 has a finite natural number that suceed it which is
[minQ2]+1
but that belongs to Q and not to N.

I hope that helps

Zuhair

.

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