ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")
Andrew Warren email (remove spam text)
"Thomas McGahee" <SIGMAIS.COM> wrote, over and over and tom_mcgahee
> Whether you like it or not, mathematically the mumber 1 exactly
> equals .9 repeating.
and David VanHorn <MITVMA.MIT.EDU> replied: PICLIST
> That's as nonsensical as saying that 2=3 for large values of 2.
> 0.99(followed by any finite or infinite number of nines) is by
> definition, not equal to 1.0
> The value of 0.99(inf..) is less than 1.0 by an infinitely small (but
> non-zero) amount.
[Sorry to single you out, Dave; this applies not only to you,
but to everyone else who's posted essentially the same thing.]
It's been a long time since I've written a "God DAMN it, you peopole
are pissing me off" email to the PICLIST, and since James Newton has
imposed a "no profanity" rule, I guess I won't write one now.
Still, though, you people ARE pissing me off. 0.9 repeating IS
exactly equal to 1. Someone posted a simple algebraic explanation
earlier; was that TOO simple? Here, for your edification, is a more
complex explanation, courtesy of the sci.math FAQ (where the
"0.999... = 1" question used to be #1 on the list):
11Q: Why is 0.9999... = 1?
A: In modern mathematics, the string of symbols "0.9999..." is
understood to be a shorthand for "the infinite sum 9/10 + 9/100
+ 9/1000 + ...." This in turn is shorthand for "the limit of the
sequence of real numbers 9/10, 9/10 + 9/100, 9/10 + 9/100 +
9/1000, ..." Using the well-known epsilon-delta definition of
limit, one can easily show that this limit is 1. The statement
that 0.9999... = 1 is simply an abbreviation of this fact.
--- 9 --- 9
0.999... = > ---- = lim > ----
--- 10^n m->oo --- 10^n
Choose epsilon > 0. Suppose delta = 1/-log_10 epsilon, thus
epsilon = 10^(-1/delta). For every m>1/delta we have that
| m |
| --- 9 | 1 1
| > ---- - 1 | = ---- < ------------ = epsilon
| --- 10^n | 10^m 10^(1/delta)
| n=1 |
So by the (epsilon-delta) definition of the limit we have
lim > ---- = 1
m->oo --- 10^n
Does that make it clearer?
It's a basic mathematical FACT that 0.9 repeating is equal to 1. If
you don't "get" this, ask questions. Say, "Gee, that sure seems
counter-intuitive." Find your old schoolbooks and see if it's
explained there. Post a message to the sci.math newsgroup if you
want a thousand people to tell you to read the FAQ... But for God's
sake, if you just can't understand it no matter how hard you try,
don't ARGUE about it; that does nothing but advertise your
unwillingness or inability to learn.
=== Andrew Warren - ix.netcom.comfastfwd
=== Fast Forward Engineering - San Diego, CA
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