Zero over Zero - Page 3

topsquark · #31 $Old$ August 1st, 2006, 08:57 AM

Quote:

Originally Posted by Quick

Look at what you're saying, you're saying that $\frac{0}{0}=1$ at the beginning of your work, so of course at the end it will say that it's possible for $\frac{0}{0}=1$

I'm not. I'm saying that 0*(1/0) = 1 just as it would for any multiplicative inverse.

-Dan

Quick · #32 $Old$ August 1st, 2006, 08:58 AM

Quote:

Originally Posted by topsquark

Then we can't have this conversation at all. Else how do you define the operation 0/0? ALL divisions x/y are defined as x times the multiplicative inverse of y!

-Dan

I already told you, I haven't been able to define $\frac{0}{0}$ all I said was that it would be best to say $\frac{0}{0}=0$ because it shares the same properties of 0.

topsquark · #33 $Old$ August 1st, 2006, 09:02 AM

Quote:

Originally Posted by Quick

I already told you, I haven't been able to define $\frac{0}{0}$ all I said was that it would be best to say $\frac{0}{0}=0$ because it shares the same properties of 0.

And I simply gave you a counter-argument that says it doesn't have to.

-Dan

Quick · #34 $Old$ August 1st, 2006, 09:06 AM

Quote:

Originally Posted by topsquark

And I simply gave you a counter-argument that says it doesn't have to.

-Dan

but your counter argument doesn't work... (at least Soltras agrees with me)

topsquark · #35 $Old$ August 1st, 2006, 09:08 AM

Quote:

Originally Posted by Quick

but your counter argument doesn't work... (at least Soltras agrees with me)

Aside from the whole problem of 0/0 existing in the first place, what specifically is wrong with it? If it's about the multiplicative inverse argument, I got that from the structure of the definition of division, which is required to give any sort of meaning to 0/0. It's a standard construction method.

-Dan

Quick · #36 $Old$ August 1st, 2006, 09:10 AM

Quote:

Originally Posted by topsquark

I'm not. I'm saying that 0*(1/0) = 1 just as it would for any multiplicative inverse.

-Dan

For the last time, write it all out and you'll find your flaw:

$0\cdot\frac{1}{0}=\frac{1\cdot0}{0}=\frac{0}{0}$

this is what your trying to do:

$0\cdot\frac{1}{0}=\frac{1\cdot0}{0}=\frac{1\cdot \not 0}{\not0}=1$

but that would only work if you say 0/0 equals 1

alright, the blasphemous thing you've been ignoring, the identity element for zero is not 1

topsquark · #37 $Old$ August 1st, 2006, 09:19 AM

Quote:

Originally Posted by Quick

For the last time, write it all out and you'll find your flaw:

$0\cdot\frac{1}{0}=\frac{1\cdot0}{0}=\frac{0}{0}$

this is what your trying to do:

$0\cdot\frac{1}{0}=\frac{1\cdot0}{0}=\frac{1\cdot\not0}{\not0}=1$

but that would only work if you say 0/0 equals 1

alright, the blasphemous thing you've been ignoring, the identity element for zero is not 1

Look, this is exactly the point I was trying to make. At no point was I cancelling zeros! In my derivation the 1 was on the RHS and the 0/0 on the LHS. All I did in the first line above was to say that 1*0 = 0. I never used your second line.

If you are going to argue a meaning for 0/0 then you have to look at what the meaning of x/y is. x/y is DEFINED to mean x*(1/y) where 1/y is the multiplicative inverse of y. So if 0/0 is allowed to exist then 1/0 exists and is the multiplicative inverse of 0. Thus 0/0 = 0*(1/0) = 1. I am simply using that fact.

My second point: The whole reason we can even have this argument is that there is NO Mathematically logical way to define and use 0/0 because such an entity cannot be rigorously defined. If it could then both of our arguments would lead to the same answer and they don't.

-Dan

c_323_h · #38 $Old$ August 1st, 2006, 09:31 AM

what would happen if 0/0 was defined? would it screw math up or shed light in other areas of mathematics? do you think $\frac{0}{0}$ will remain undefined forever, or do you think a courageous mathematician will come along and challenge this convention? i think people/mathematicians hundreds of years from now will have figured out what 0/0 is and look back and wonder why it took us so long.

Like Einstein said, "Imagination is more important than knowledge."

That was someone's signature don't remember who's it was though.

Quick · #39 $Old$ August 1st, 2006, 09:32 AM

Quote:

Originally Posted by topsquark

Then
$\frac{1}{0} \cdot 0 \cdot \frac{1}{x} = \frac{1}{0} \cdot 0$

$\frac{1}{0} \cdot 0 \cdot \frac{1}{x} = 1$ (RHS Property of multiplicative inverses.)

How are you turning the RHS of your equation into 1?

topsquark · #40 $Old$ August 1st, 2006, 09:34 AM

Quote:

Originally Posted by Quick

How are you turning the RHS of your equation into 1?

If 0/0 is defined to exist, then by the definition of division 1/0 exists and is the multiplicative inverse of the real number 0. The product of any real number and it's multiplicative inverse is defined to be 1. Thus
$0 \cdot \frac{1}{0} = 1$ by definition.

-Dan

Quick · #41 $Old$ August 1st, 2006, 09:37 AM

Quote:

Originally Posted by topsquark

If you are going to argue a meaning for 0/0 then you have to look at what the meaning of x/y is. x/y is DEFINED to mean x*(1/y) where 1/y is the multiplicative inverse of y. So if 0/0 is allowed to exist then 1/0 exists and is the multiplicative inverse of 0. Thus 0/0 = 0*(1/0) = 1. I am simply using that fact.

-Dan

your absolutely right, y/y = y(1/y) = 1
but here's why:
$\frac{y}{y}=1$
but now we see that with zero there is no definition (yet) of zero over zero, therefore you CANNOT say that $\frac{0}{0}=0\cdot\frac{1}{0}=1$

topsquark · #42 $Old$ August 1st, 2006, 09:38 AM

Quote:

Originally Posted by c_323_h

what would happen if 0/0 was defined? would it screw math up or shed light in other areas of mathematics? do you think $\frac{0}{0}$ will remain undefined forever, or do you think a courageous mathematician will come along and challenge this convention? i think people/mathematicians hundreds of years from now will have figured out what 0/0 is and look back and wonder why it took us so long.

Like Einstein said, "Imagination is more important than knowledge."

That was someone's signature don't remember who's it was though.

If 0/0 were to be defined it would have to be in a system that is more restricted than the field of real numbers. I'm not saying it would be impossible to construct such a set of numbers (though admittedly it's beyond my powers to imagine!)

I simply don't see any value to it since, as ThePerfectHacker suggested (either in this or a different thread), 0/0 as a valid entity would be a "restriction" of sorts on the field of Mathematics, not an "expansion" like the number i was.

-Dan

topsquark · #43 $Old$ August 1st, 2006, 09:54 AM

Ooops, accidentally edited this rather than quoted - result (with profuse
apologies) I lost the original content

CaptainBlack
(RonL)

(Added by topsquark) AAARRGGGHH!! Probably for the best as I introduced notation and conceptualizations that Quick probably hasn't seen yet.

-Dan

CaptainBlack · #44 $Old$ August 1st, 2006, 10:30 AM

Quote:

Originally Posted by topsquark

Ooops, accidentally edited this rather than quoted - result (with profuse
apologies) I lost the original content

RonL

What I had intended to post is:

Meta argument that 0/0 should be undefined.

If there were a suitable unambiguous definition for all seasons, then this thread would not be so long, Hence 0/0 is undefined QED.

RonL

ThePerfectHacker · #45 $Old$ August 1st, 2006, 10:36 AM

Quote:

Originally Posted by c_323_h

what would happen if 0/0 was defined? would it screw math up or shed light in other areas of mathematics? do you think $\frac{0}{0}$ will remain undefined forever, or do you think a courageous mathematician will come along and challenge this convention? i think people/mathematicians hundreds of years from now will have figured out what 0/0 is and look back and wonder why it took us so long.

Like Einstein said, "Imagination is more important than knowledge."

That was someone's signature don't remember who's it was though.

Dude, I know what I am talking about. I said you cannot define it without destroying the important distributive property. Also, if you do all you number system to have a inverse for the identity element it would be an unconvential system (you can do that, in fact, I once tried and it was worthless).

It is basicallly, the same thing as saying.
"Let there be a courages mathematician who can express the square root of two as a rational number".