piclist 2001\06\02\232157a >
Thread: ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")
www.piclist.com/techref/index.htm?key=brain+burp+rounding
BY : Jim Paul email (remove spam text)

who cares?
-----Original Message-----
From: Andrew Warren <fastfwdIX.NETCOM.COM>
To: PICLISTMITVMA.MIT.EDU <PICLISTMITVMA.MIT.EDU>
Date: Saturday, June 02, 2001 10:14 PM
Subject: [OT]: ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")

"Thomas McGahee" <tom_mcgaheeSIGMAIS.COM> wrote, over and over and
over:

> Whether you like it or not, mathematically the mumber 1 exactly
> equals .9 repeating.

and David VanHorn <PICLISTMITVMA.MIT.EDU> replied:

> 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.

oo              m
---   9         ---   9
0.999... = >   ---- = lim  >   ----
--- 10^n  m->oo --- 10^n
n=1             n=1

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

m
---   9
lim  >   ---- = 1
m->oo --- 10^n
n=1

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,
unwillingness or inability to learn.

-Andy

=== Andrew Warren - fastfwdix.netcom.com
=== Fast Forward Engineering - San Diego, CA
=== http://www.geocities.com/SiliconValley/2499

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<000901c0ebda\$6eb30dc0\$25a3a3d1@jim> 7bit