www.piclist.com/techref/index.htm?key=brain+burp+rounding

"Thomas McGahee" <EraseMEtom_mcgaheeTakeThisOuTspamSIGMAIS.COM> wrote, over and over and

over:

> Whether you like it or not, mathematically the mumber 1 exactly

> equals .9 repeating.

and David VanHorn <KILLspamPICLIST@spam@spamMITVMA.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,

don't ARGUE about it; that does nothing but advertise your

unwillingness or inability to learn.

-Andy

=== Andrew Warren - STOPspamfastfwd.....RemoveMEix.netcom.com

=== Fast Forward Engineering - San Diego, CA

=== http://www.geocities.com/SiliconValley/2499

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In reply to: <4.3.2.7.2.20010602195732.00ced4f0@mail.cedar.net>

See also: www.piclist.com/techref/index.htm?key=brain+burp+rounding