Re: Interesting math

On Sun, 15 Jul 2007 23:10:24 -0700, Purl Gurl
<purlgurl@xxxxxxxxxxxx> wrote:

Hatunen wrote:

Al in Dallas wrote:
blmblm wrote:
Purl Gurl wrote:

6 / 0 = [infinite number set]
6 = [infinite number set] * 0

Division by zero is defined as undefined. This is not true.

Division by zero is undefined. Anyone who has even dabbled in
basic number theory knows that. And division by zero does not
create an infinite number for that reason. What we CAN say is
that as the divisor approaches zero the result grows larger and
larger. It's tempting to say the result approaches infinity, but
it would be wrong since infinity can never be approached: all
finite numbers are the same "distance" from infintiy.


No, division by zero is easily defined. Think Zeno.

Interesting you should mention Zeno. He did not define division
by zero, but he did introduce the concept of approachig zero, as
described in the part of my post you deleted.

Division by zero yields an infinite number set. An infinite
number set cannot be defined although many claim infinity
is where parallel lines meet, which is rather humorous.

Please tell us what you mean by "infinite number set". Be
as specific as you can.

Infinite number sets were defined long ago by Georg Cantor. See,
e.g., http://scidiv.bcc.ctc.edu/Math/infinity.html


A rather fun page. I enjoyed reading material there. Should you
follow the Zeno link, you will discover the very basis of my
playful contention division by zero yields an infinite number set.

I don't see a Zeno link. In any case, Aeno does not represent the
sort of mathematical rigor required today to say the division bty
zer is defined; it isn't save anecdotally.

"So a crucial assumption that Zeno makes is that of infinite divisibility...."

"Infinite divisibility is not the same as dividing by zero.
The next paragraph points out the limitations of what Zeno said.
Ultimately his argument comes down to the concept of approaching
zero but not reaching it. This is fundamental to differential
calculus.

I am a little surprised none caught onto my use of Zeno thinking.

I suspect many of us are aware of Zeno's Paradox, which has been
neatly disposed of by differential calculus.

However,
I did not drop any direct clues of this. Zeno correctly thinks in terms of
increasingly smaller divisions, conversely larger divisions. Same is true
for zero; a number can be divided by zero an infinite number of times.

No. He doesn't say that. But in the text that your quote above
comes from it says Zeno *assumed* something like that.

Delights me to read others continuing this zero debate.

For mathemeticians, there's no debate. In this thread it's pretty
much laymen leaping to conclusions.

Equally delightful, on your provided link and over the centuries, are
attempts to define infinity. Decades back one of my science teachers said,
"Infinity is where parallel lines meet." This definition works well.

Infinity is well-defined since the days of Cantor. High school
science teachers rarely know enough science or mathematics to
understand this.

For easy reading for laymen, I suggest George Gamov's book "1, 2,
3 Infinity", a book form the 1950s that is so popular on the
subject it is still in print.

--
************* DAVE HATUNEN (hatunen@xxxxxxx) *************
* Tucson Arizona, out where the cacti grow *
* My typos & mispellings are intentional copyright traps *
.

Relevant Pages

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  • Re: John Gabriels Theorem Revisited.
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  • Re: You Dont Have to Be Nuts to Be a Mathematician ...
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  • Re: Forth PARANOIA
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  • Re: Interesting math
    ... And division by zero does not ... it would be wrong since infinity can never be approached: ... Think Zeno. ... Delights me to read others continuing this zero debate. ...
    (alt.usage.english)