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Authored by: cjk fossman on Friday, December 14 2012 @ 12:39 PM EST |
What if my limit is .01 multiplied by an infinite series of
nines?[ Reply to This | Parent | # ]
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Authored by: Anonymous on Friday, December 14 2012 @ 12:51 PM EST |
It is axiomatic that there is one number (really, an infinity of numbers)
between any two numbers that are different.
It is simple to prove that there is no number between 1.99... and 2.
You can't distinguish between "2" as a finite representation of a
number and "1.99..." is an infinite representation, because, in fact,
nobody has had any trouble at all representing the finite decimal calculation as
a finite number of digits (using some repetition indicator).
Nor can you give decimal notation any special pride of place. There are other
continuing-fraction representations that generate an infinite calculation
leading to EVERY rational number.
On the other hand, in engineering class you don't talk about numbers at all. You
only talk about finite ranges of numbers. you don't have any occasion to use the
number "2", you merely use "2.0" as a
convenient-but-possibly-misleading shorthand for "somewhere between 1.95
and 2.05".
Accountants have a touching faith that they do NOT use numbers like engineers
do. They are wrong (their concepts of "number" for practical purposes
being pretty reliably wrong in every way)--and their error is what makes
"salami-slicing" frauds so easy to perpetrate.[ Reply to This | Parent | # ]
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