# Division by zero. Go ahead and laugh.

Discussion in 'Undergraduate Math' started by Lefty, Oct 7, 2004.

1. ### LeftyGuest

Thanks. I suppose you're probably right.

If you're feeling at all sympathetic you could help me out by weighing in
and straightening me out a little.

Lefty, Oct 8, 2004

2. ### LeftyGuest

There are no paradoxes or inconsistencies in mathematics, unless you
remove

Thanks Dave, but the reference to JH, now that stings a little.

OK, x+3=0. No solution. No problem. Is this a singularity for addition on R
? I honestly dont know.

I'm _not_ saying that 1/0 = infinity. All I am saying is that leaving it
"undefined" is the equivalent of waving magic wands. I dont think that it's
good at all.

What I said what that 1 / 0 = [inconsistency] or 1 / 0 = [paradox] ,
or something to that effect.

Trying to gain some focus here so bear with me please.

Thanks.

Lefty, Oct 8, 2004

3. ### LeftyGuest

Division by zero creates an inconsistency in arithmetic, and any result
can

I'm saying that it seems that there is something being missed by leaving it
"undefined".

If 1/0 => [inconsistency], then there should be a formal language or
symbology to state that when you divide by zero you get a paradox or an
inconsistency. There should be some way of stating this formally using
_algebra_ . Not paragraphs of english. Algebra would be more complete, and
the whole thing might lead to new knowledge.

I'm guessing, but it's all just fun.

Lefty, Oct 8, 2004
4. ### LeftyGuest

It has given me much appreciated insight.

Numbers are metaphysical entities. They are abstractions. I am not sure if
these quantities can really be said to exist in the physical universe.
Obviously they seem to, but this would make an enormous argument.

However, there are two numbers which seem to fit the physical world almost
perfectly. Zero and 1. I wont bore you with my musings except to say that
when considering these numbers, it is almost as if the abstract world is
bridged to the physical universe by the existence of zero and 1. Zero and 1
must exist in the real world. It almost resembles the dichotomy of
existence, true or false.

Certainly you can have 1 banana. And certainly you can have zero bananas.
The other numbers are all quite dubious in the real world.

Might have something to do with why there are singularities. Or maybe it's
the whiskey talkin' ?

Who knows.

Lefty, Oct 8, 2004
5. ### robert j. kolkerGuest

One is not "leaving" anything undefined. One is showing that 1/0 cannot
be defined in a consistent division ring. Just because something that
looks like a valid alebraic formula can be written, does not mean it is
a valid algebraic formulate.
I have already demonstrated this. Now pay attention. 1/0 = x means that
1 = 0*x. But 0*x = 0, which implies that 1 = 0, which is a
There should be some way of stating this formally using

See my previous 3 lines.

It is no fun to make a pain in the ass of yourself. I have produced the
demonstration you asked for. Now shut up.

Bob Kolker

robert j. kolker, Oct 8, 2004
6. ### robert j. kolkerGuest

Just when we thought Plato was dead and buried, you shoed up. Go away.

Bob Kolker

robert j. kolker, Oct 8, 2004
7. ### N. SilverGuest

I claim: 1/0 = infinity, 0/0 is an undetermined form,
and -1/0 = minus infinity.

However, infinity and minus infinity are not real
numbers. So, in the real numbers, i.e., those
numbers in one-to-one correspondence with
points on the real line, 1/0, 0/0 and -1/0 are
undefinied.

N. Silver, Oct 8, 2004
8. ### N. SilverGuest

I claim: 1/0 = infinity, 0/0 is an undetermined form,
and -1/0 = minus infinity.

However, infinity and minus infinity are not real
numbers. So, in the real numbers, i.e., those
numbers in one-to-one correspondence with
points on the real line, 1/0, 0/0 and -1/0 are
undefined.

N. Silver, Oct 8, 2004
9. ### KeckmanGuest

No no. That sounds interesting. Please Lefty tell us more.

Keckman, Oct 8, 2004
10. ### LeftyGuest

Lefty, you don't know what you are talking about.

Yes, I know. I'm not arguing that division by zero should be allowed. I am
arguing that it is not being leveraged. I am arguing that there is a wealth
of information hidden behind this funky, freaky thing, this contradiction,
this paradox. I think that there is something mysterious about it which has
not been revealed.

Or maybe I just have'nt read enough ? Singularity theory maybe ?

Lefty, Oct 8, 2004
11. ### LeftyGuest

Thanks Bob, but I think that you took me out of context.

Lefty, Oct 8, 2004
12. ### LeftyGuest

I believe that the lim 1/x as x->0 is infinity. Am I wrong ?

Really guys, I'm rusty, so bear with me a little.

In the above, we're talking about 2 different things however.

1) Mathematical operations which exist as abstractions, and

2) Manipulations in the physical world which resemble mathematical things.

It would be nice to bridge these solidly. Never been done I think,

Lefty, Oct 8, 2004
13. ### LeftyGuest

it will probably show up on one of those "usenet crank" websites, who cares.

I reserve the right to imagine whatever the hell I please. Let freedom
reign.

Lefty, Oct 8, 2004
14. ### LeftyGuest

Lets say that you wanted to make a fundamental mathematical statement about
the physical universe. Please take a look at this axiom. I think that it
says something about numbers and theri relationship to the physical
universe.

Maybe I lost my mind, I dont care. Please tell me what you think.

----------------------------------------------

Axiom
No two objects in the physical universe can ever be identical. Even if they
are identical in every respect, they still occupy two separate locations,
again making them different. You can have one of something, and you
can have zero of something, but that's all, because no two objects can
ever be identical.

Proof.
suppose not,
qed,
bla bla bla

Lefty, Oct 8, 2004
15. ### David W. CantrellGuest

Gosh, it's very curious then that complex analysis texts which discuss C*,
the one-point compactification of C, define 1/0. It's truly amazing that
they do what cannot be done! What a mistake! Will you perhaps take it
upon yourself to inform the authors of such texts of their horrid error?

Of course, instead of doing that, it would actually be much more profitable
for you to think about why you are incorrect in claiming, bluntly, that 1/0
cannot be defined. (Hint: In systems allowing division of nonzero
quantities by zero, division is not defined as you have indicated.)

David Cantrell

David W. Cantrell, Oct 8, 2004
16. ### David W. CantrellGuest

Hmm. Since you seem to be mentioning "infinity" and "minus infinity" as
separate entities, it would seem that you're thinking about the two-point
compactification of R. But 1/0 is normally undefined in that system.

In the one-point compactification of R, however, we have

x/0 = unsigned infinity for all nonzero x.

David Cantrell

David W. Cantrell, Oct 8, 2004
17. ### Richard HenryGuest

x = -3.

Richard Henry, Oct 8, 2004
18. ### Richard HenryGuest

There is no limit to 1/x as x increases without bound.

Richard Henry, Oct 8, 2004
19. ### Miro JurisicGuest

Yes. In order for lim f(x) as x -> a to be defined, the following has to be true:

For every sequence x1, x2, x3, ... whose limit is a, the limit of sequence
f(x1), f(x2), f(x3), ... is the same. Then lim f(x) as x -> a is the same as the
limit of any of those sequences f(x1) etc.

However, 1/x as x->0 over positive numbers is large and positive, whereas 1/x as
x->0 over negative numbers is large and negative. This makes lim 1/x as x->0
undefined.

For example, consider this sequence of values of x:

1, -1/2, 1/3, -1/4, 1/5, -1/6, ...

Clearly, limit of that sequence is zero. Now compute 1/x at those points:

1, -2, 3, -4, 5, -6, 7, -8, ...

That is not a convergent sequence. It has no limit.

meeroh

Miro Jurisic, Oct 8, 2004
20. ### KeckmanGuest

Hey. I'm clad i found "friends" here because i too like to wonder things
like that.

I do not agree you. I think what comes to amounts there can only be one.
That there isn't any something is nothing. It is nonsense. Zero is not a
number.

That's why i observe the Naturals starting from number 1, not from zero,
like
Peano did.

But what i think there is: there is true and false, on/off. And sometimes
those are meaned like numbers one and zero, but in deeper understanding
they are not.

In universum something exist. And it's amount is 1. We can't count those
things that does not
exist.

Let's go ahead...If you have any agrees/not agrees, tell.

Keckman, Oct 8, 2004