ENOUGH! (was: "Re: [OT]: Brain Burp Rounding??")
Paul Hutchinson email (remove spam text)
First, I'd like to thank everyone for their comments on this topic. They
have made me review and re-think the basic concepts of mathematics in
general. I've spent way too much time in the past few days re-reading text
books and searching for other texts on the various fundamental algebraic
operations, definitions and, axioms. However, I don't consider this wasted
time because I firmly believe that blind faith in anything is bad and, I
have not reviewed the fundamentals in the past decade or two.
I especially would like to thank Dave V. for the link to Swarthmore Colleges
excellent Dr. Math project. http://forum.swarthmore.edu/dr.math
There is only one thing I feel comfortable stating with 100% certainty after
my research and review.
If you are a student and the question of, does .999... = 1, comes up on a
test, answer Yes.
I could not find one single reference by any professor/teacher/school
district/college or university that would allow you to answer no and be
given credit for a correct answer. The most complete web resource for info
on this topic I found is,
http://forum.swarthmore.edu/dr.math/faq/faq.0.9999.html. If you read the
page be sure to also read the five linked pages at the end of the FAQ
> The root problem here appears to be that there some numbers which the
> decimal system is ill equipped to represent, in a manner similar to roman
> numerals having problems with large numbers, only in a deeper manner.
> 1/3 is easy to deal with, but can't be represented with complete accuracy
> in decimal form.
This statement has brought much needed closure in my mind as to what the
objections are to the simple algebraic proof I presented in a post last
week. I had been wondering what step(s) in the proof were potentially
flawed. From this statement I see that the disagreement comes with the very
first statement of the proof.
x = 0.9(repeating)"
The problem is that repeating decimals are considered by some to not be
accurate representations of numbers like 1/3. This statement appears to be
somewhat supported by the work of Georg Cantor from the late 19th century.
For 1/3 to be <> 0.333... all that needs to be true is that long division
does not work in some cases. Personally I don't believe this but to my mind
it is certainly possible that at some point in the future this may be proven
to be the case. After all similar events have happened regularly throughout
the course of human history. For those interested I recommend James Burkes,
"The Day the Universe Changed" either the book or television series from the
I have decided that in the future if a question regarding repeating decimal
representations of fractions comes up on the PICLIST, I will ask if the
questioner believes that 0.333... = 1/3. If they do I'll try to help but if
they don't I'll ask that the question be restated without the need for
repeating decimals before attempting to help.
PS - I was a bit shocked by some of the assertions that mathematics is all
magic tricks, I had thought that everyone accepted mathematics as the
official language of science and felt there was no magic to it. I do expect
people to look skeptically at things but to attribute magic to anything is
way more than I can accept.
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