Multiplication by zero

[Guest Doron Shadmi]

It is so ill written that it is really hard to make sense of.

Please look at #17 and give some example that clearly shows why my original point of view about 0*oo is ill written.

[Dave]

Sure. What exactly do you define the "concept of length" to be? A cursory glance doesn't give much in terms of a mathematical definition.

[MandrakeRoot]

Sure. What exactly do you define the "concept of length" to be? A cursory glance doesn't give much in terms of a mathematical definition.

 

IT is exactly this sort of thing that makes it ill writen. I totally agree with you dave. Doron you introduce concepts without defining them and expect people to see them the same way that you do, if we dont think similar about your concepts there is no way we can follow your reasoning.

 

Mandrake

[Guest Doron Shadmi]

It is very simple Dave.

 

My length concept is not a geometrical concept but based on the Function concept as the 1-1 mapping.

 

Length 0 is the 1-1 mapping of an element to itself, where Length NOT= 0 is the 1-1 mapping between at least two distinguished elements.

 

The minimal information form that we get in the case of 0 Length, is a Point {.} .

 

The minimal information form that we get in the case of Non_0 Length, is a Segment {._.} .

 

The difference between a Segment's Edge and a Point, can be found here:

 

http://www.geocities.com/complementarytheory/SegPoint.pdf

 

 

If you don’t understand it yet, then consider that No_Length_at_all has Rank 0 where a Length has Rank 1 (http://mathworld.wolfram.com/Rank.html), for example:

 

{} (No_Length_at_all)

 

{.} 0 Length (Point)

 

{} <--Length--> {{}} is a 1-1 mapping between at least two distinguished elements (Segment)

 

{__} Non-measurable Length (Fullness)

 

 

Each building-block {}, {.}, {._.}, {__} is a free element (not composed by the other building-blocks).

 

Now please re-read my original answer (#17) about 0*oo problem.

 

Thank you.

[Sayonara]

Back on topic please.

[matt grime]

oh, and 0 times infinity still equals 0.

 

 

In what sense are you using "times" and how does this affect the Reals? What exceptions to the usual field axioms, which we still presume hold for all other defined operations, do you now need to inttoduce in order to give a complete decription of all of the newly valid operations on he reals?

 

NB I don't care about any handy wavy heuristic "real life" arguments, it is only the mathematical consistency that counts, especially as there is little "real life" about infinity when treated as a number in this casual fashion.

[123rock]

Ok' date=' was hoping not to have to use this, but i can add up zero infinitely many times and get any number you care for. it's called measure theory.

 

all these questions have been asked before, they have answers, they are understood, and they all are limited by exactly what they claim to be.

 

 

you can extend the numbers to allow a limited arithmetic with infinity, however 0/0 and 0*inf are still not permitted in that system because there is no consistent or necessary way of assigning a MATHEMATICAL meaning to them.

 

Nothing more nor less. there is no mystery or great con trick going on here.

 

you don't make a right on a red light in New York, but you do in California, so if you're in california make that right, and when you're in new york don't. simple set of rules just like mathematics is. apart from the simple bit.

 

don't confuse mathematics with its application in modelling something.

 

0*5 is not what you've got if you've got no lots of 5 apples.

 

1*x=x for all non zero x in R, 0+x=x for all x in R, using this we can consistently define 1*0=0 since

 

1*0=1*(0+0) =1*0+1*0, subtract 1*0 and we get 1*0 =0

 

 

as for callipygous, those three squirrels, are they the same squirrel or 3 different squirrels? what's even a squirrel really? red or grey? why not another rodent very much like a squirrel?[/quote']

 

You can start by seeing some properties of the concept of infinity. For example 1/infinity=0 is a well known fact:

 

1/9=0.111...1

1/9(9)=(9)0.111...1

9/9=0.999...9

1=0.999...9

1-0.999...9=0

0.000...1=0

 

0.000...1 being 1/infinity.

 

We can see a relationship by the concept of infinity even though it is not a number.

 

An interesting post I found somewhere on the net:

 

assume infinity=x, then 1/x=0; 0/0=(1/x)/(1/x), 0/0=infinity/infinity

 

This has several flaws, including the fact that it assumes that [1/x]/[1/x]=[1/x]*x, or that infinity's reciprocal is 0, which would mean that infinity*0=1

 

Again, infinity has no reciprocal, since [1/x]x=[0]x

 

0*infinity, I think that's what the discussion was about would equal infinity/infinity or 0*x=x/x

 

if infinity/infinity=1, then [infinity/infinity]2=2, and infinity/infinity=2, replacing infinity/infinity with 1, 1=2.

 

This excludes all number except for 0.

So infinity*0 might be 0.

[gene]

my answer would be infinity.

 

Infinity is inclusive of zero.