Re: The infintely small number b
- From: Venkat Reddy <vreddyp@xxxxxxxxx>
- Date: Fri, 16 Nov 2007 19:37:58 -0800 (PST)
On Nov 17, 8:21 am, Venkat Reddy <vred...@xxxxxxxxx> wrote:
Following is the definition and properties of the infinitely small
number b which I called sookshma number in my recent posts. This may
also be called infinitesimal, but I'm not sure if the formal
definition and properties of infinitesimal are the same. I'm using b
as the symbol for this, simply because it was used in the recent
discussions.
I knew this definition is neither rigorous nor complete, but I think
it has the essential ingredients to make it more formal.
The infinitely small number b
-----------------------------
b is the number that represents smallest extent.
b is not equal to zero because zero represents non-existence of
extent, while b represents existence of extent.
b is not equal to b in arithmetic sense (addition, subtraction).
b is equal to b in geometric sense: b*1 = b; This simply means that b
exists
Operations with zero (non-existence of extent)
b + 0 = b
b - 0 = b
b * 0 = 0
(b / 0) is undefined and not to be taken as inf.
Operations with itself
b + b = b
b * b = b
b / b = 1
Correction: (b / b) must be undefined too.
(b - b) is undefined.
Operations with n where b<n<inf:
n * b = b
n / b = inf. (indicates that n/0 is undefined and can not be taken as
inf.)
n + b = n + b
n - b = n - b
We can't precipitate the last two arithmetic operations (addition,
subtraction) because it requires comparison of b with b itself in
arithmetic sense which is undefined.
- venkat
.
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