Multiplication by zero

[Muhammad Ali]

As we all know that multiplication of a number by zero results in zero.

What happens if zero is multiplied by infinity

[Cap'n Refsmmat]

Infinity is not a number. Infinite just is when it is never ending.

[VendingMenace]

i don't really know the absolutely correct answer, but i will give it a shot anywho

 

multiplication is really just a easy way to add up numbers. That is, 6*2 = 2 + 2 + 2 + 2 + 2 + 2 . Right?

 

Another way of looking at this (removing some of the abstract-ness) is as if i had 6 twos then how many do i have? Of course the answer is twelve.

 

So then we can ask ourselves, if i have zero infinities, what do i have. Well, you have nothing. Since you have zero of them.

 

So i would hazard to guess that 0 * infinity = 0

 

But like i said, i am not really a mathamatician, so this could be wrong.

[matt grime]

Once more the question is ill posed as all these things are.

 

Multiplication is dependent on the set (RING) we're talking about. Infinity isn't in the RING of integers, or rationals, or reals or complexes.... and so asking what infinity times zero is is exactly as meaningful as asking what 3 times squirrel equals, it just looks more plausible, unless *you* specify what *you* mean by multiply.

[Treadstone]

Once more the question is ill posed as all these things are.

 

Multiplication is dependent on the set (RING) we're talking about. Infinity isn't in the RING of integers' date=' or rationals, or reals or complexes.... and so asking what infinity times zero is is exactly as meaningful as asking what 3 times squirrel equals, it just looks more plausible, unless *you* specify what *you* mean by multiply.[/quote']

 

i would imagine he just referring to regular real number multiplication

[AL]

i would imagine he just referring to regular real number multiplication

As matt grime already pointed out though, [math]\infty[/math] is not in [math]\Re[/math], so the multiplication is still undefined.

[matt grime]

Exactly, AL.

 

I can define the symbol 0*inf to be anything I choose. The problems arise when I try and make this consistent with the properties of other multiplications in that ring: there is no useful way of doing this so we don't bother as it is unnecessary.

 

Let me give a silly analogy (there are no good analogies as we all know)

 

Why isn't there a single word in the English Language that means 'yellow stone eating monster that lives at the centre of the Earth'

 

i could possibly invent one etymologically, say,

 

ge'centric'etio'pedi'phag'osaur

 

but that doesn't mean I've done anything good or useful.

[ed84c]

this suggests that 0 is somehow stronger than infinity. Is there any grounds for 0*infinity=1, if you use 0/0 to equal 1?

[Gilded]

Heh, one off-topic question came to mind about the stone eating: is an organism that consumes minerals (and only minerals, no organics whatsoever) as they are in the soil be a "lithovore"?

[Guest Doron Shadmi]

Oops, some reply problems.

 

Anyway, please look at #17

[VendingMenace]

this suggests that 0 is somehow stronger than infinity.

 

What does??? I thought all the cool math people just got done explaining that 0*inifinity is a meaninless concept' date=' the operation is not defined, and has no real value in math?

 

how does this suggest that 0 is stronger than infininty?

 

Is there any grounds for 0*infinity=1, if you use 0/0 to equal 1?

 

But the question is does 0/0=1? Which i don't know, buti suspect that the answer to this operation is undefined so i don't think it would really matter.

 

But even if 0/0=1 why would this change anything? 2*8=16 does the fact that 2/2 =1 change anything intrinsic about the number 2?

[Callipygous]

Once more the question is ill posed as all these things are.

 

Multiplication is dependent on the set (RING) we're talking about. Infinity isn't in the RING of integers' date=' or rationals, or reals or complexes.... and so asking what infinity times zero is is exactly as meaningful as asking what 3 times squirrel equals, it just looks more plausible, unless *you* specify what *you* mean by multiply.[/quote']

 

3 times squirrel is 3 squirrels... duh.

 

but anyway. like the first dude said. if you have zero infinities how much do you have? zero.

[matt grime]

Ok, 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?

[ed84c]

how does this suggest that 0 is stronger than infininty?

 

Well, if we look a this NOT mathematically, it would appear that 0 and infinity are 2 (almost menigless) points on the opposite end of a spectrum. If we combine them and they equal 0 it means, that, allthough not a mathematical and quite difficult concept to grasp, 0 is stronger, in other circumstances they ALWAYS make values themselves (0*2=0 etc.) when multiplied and obviously the opposite when divided.

 

Im NOT a mathematician, its just an outsider view that it looks like to me.

[WaR]

Well, zero is a number and Infinity is not a number. So, you can't really compare both.

[MandrakeRoot]

You can always define what you like. The most important question is if what you define makes sense. You can extend the real numbers by adding infinity to the set of real numbers as an element and then define 0*infinity to equal pi, but that would

not make much sense.

 

Mandrake

[Guest Doron Shadmi]

Let us think about another option.

 

Let us say that any positive number is based on the Length concept.

 

It means that if the Length concept itself is omitted, then our set is Empty and we get {}, which is the Empty set.

 

By saying “0 length” we are using the Length concept and in this case we get number 0, which is equivalent to a Point.

 

Any other number, which is not a point, is at least some Segment, which is always longer than a Point.

 

We can take any arbitrary segment and call it 1.

 

Now we have two building-blocks that can help use to define any given positive R member that we wish.

 

From this point of view any given positive number, which is not 0 can be represented as the right edge of a segment, which its value defined relatively to the left 0 edge of the segment, and relatively of what has been chosen by us to represent 0_1, which is number one.

 

So our positive R members are based on the Length concept, and each one of these numbers has a unique length, that can be represented by a point {.} or by a segment {._.} .

 

Now let us check what is infinity according to this approach.

 

We know that {} means that the Length concept itself is omitted from our framework.

 

Can we define a state, which is the opposite of {}?

 

The answer is: Yes, and we can call this state Fullness which is the totality of the length concept itself, or in other words it is an infinitely long element that can be represented by us as {__} or {.__}.

 

It means that we cannot define its length and use it to get a particular number, or in other words, the Length concept itself is too strong to be used by us.

 

From this point of view we get these 4 basic building-blocks {} (Emptiness, which its “content” is too weak to be used as an input in this framework), {.} (Point, which is 0 length), {._.} (Segment, which is any R member > 0) and {__} or {.__} (Fullness, which its length cannot be used as an input in this framework).

 

Now let us examine Point*Fullness, which is equivalent to the original question, which is:

 

Zero*Infinity

 

My answer (according to the Length-concept framework) is:

 

What is the result of Point*Emptiness?

 

What is the result of Point*Fullness?

 

In both cases we can clearly see that we cannot get any meaningful result within this framework, because neither Fullness nor Emptiness can be used as input (or legitimate participators) in these multiplication operation.

 

(By the way, if we add the Direction concept to the above framework, we can represent the entire R members, by using x_0, 0, 0_x froms).

 

As you can see, the answer to this question from this point of view, is very simple.

[matt grime]

Let us think about another option..

 

 

Call me an overzealous bodyguard of mathematics if you will, but let's not do any such thing and let's not hijack another thread with your own personal pet theory that no one else cares about.

 

The question has been answered properly in mathematical terms which is the scope within which it was asked.

[MandrakeRoot]

Call me an overzealous bodyguard of mathematics if you will' date=' but let's not do any such thing and let's not hijack another thread with your own personal pet theory that no one else cares about.

 

The question has been answered properly in mathematical terms which is the scope within which it was asked.[/quote']

 

So what do you think of Doron Shadmi theory ?

Have you actually given it some serious thought ?

 

Mandrake

[matt grime]

I have had many discussions with Doron, most of them have now been deleted from physicsforums.com, where he often hijacked threads, hence my post to which some people's respsonses have vanished.

 

Whatever Shadmi Theory is, it is ill-presented and lacks any coherent definitions of the terms it introduces - the state it's in now constitutes a vast improvement over its original form.

 

I am tired of trying to explain to Doron the misconceptions he has about mathematics and pointing out where his unfounded allegations about its paucity were wrong.

 

Have you tried explaining why cantor's argument works to someone who doesn't even know what a bijection is?

 

Explaining that there is no such thing as the axiom of infinity induction making mathematics internally inconsistent?

 

Explaining basic logic theory to someone who thinks that if a proposition is equivalent to one of the axioms of the system that the proposition is undecidable?

 

Tried explaining that the collatz conjecture isn't equivalent to the statement 'there is an infinite set'?

 

I've done all those and it was painful; I don't intend to start again.

 

See, already this thread is being h ijacked by it.

Moderators feel free to delete my posts if you want to get this back on topic.

[Sayonara]

I have had many discussions with Doron, most of them have now been deleted from physicsforums.com, where he often hijacked threads, hence my post to which some people's respsonses have vanished.

Haggy's post was blatant flaming, and nobody is interested in reading ed84c's running commentary on posts they have already seen.

[Ophiolite]

As we all know that multiplication of a number by zero results in zero.

What happens if zero is multiplied by infinity

So' date=' as a non-mathematician I can safely conclude that if I multiply zero by infinity, I shall get a big fat non-numeric nothing, and I shall get it an infinite number of times. I'm glad we straightened that out.

 

Edit:

Well, if we look a this NOT mathematically,

Ed, you can't look at a maths issue non-mathematically. Several posters have made it clear the question has no meaning. Why are you going on? (Rhetorical question. Please don't answer.)

[Guest Doron Shadmi]

I have had many discussions with Doron' date=' most of them have now been deleted from physicsforums.com, where he often hijacked threads, hence my post to which some people's respsonses have vanished.

 

Whatever Shadmi Theory is, it is ill-presented and lacks any coherent definitions of the terms it introduces - the state it's in now constitutes a vast improvement over its original form.

 

I am tired of trying to explain to Doron the misconceptions he has about mathematics and pointing out where his unfounded allegations about its paucity were wrong.

 

Have you tried explaining why cantor's argument works to someone who doesn't even know what a bijection is?

 

Explaining that there is no such thing as the axiom of infinity induction making mathematics internally inconsistent?

 

Explaining basic logic theory to someone who thinks that if a proposition is equivalent to one of the axioms of the system that the proposition is undecidable?

 

Tried explaining that the collatz conjecture isn't equivalent to the statement 'there is an infinite set'?

 

I've done all those and it was painful; I don't intend to start again.

 

See, already this thread is being h ijacked by it.

Moderators feel free to delete my posts if you want to get this back on topic.

[/quote']

No dear Matt, you simply do not understand Included-Middle logical reasoning from an Included-middle logical reasoning point of view, because you examine it from an Excluded-middle point of view.

 

My answer to 0*Infinity That I gave in post #17, which is based on Included-middle logical reasoning, is simpler then the answer that is given by the Excluded-middle logical reasoning.

 

The standard answer (which is based on Excluded-middle logical reasoning) about 0*oo is: "unkown" (as we can see here):

 

http://mathworld.wolfram.com/Indeterminate.html

[MandrakeRoot]

I have had many discussions with Doron' date=' most of them have now been deleted from physicsforums.com, where he often hijacked threads, hence my post to which some people's respsonses have vanished.

 

Whatever Shadmi Theory is, it is ill-presented and lacks any coherent definitions of the terms it introduces - the state it's in now constitutes a vast improvement over its original form.

 

I am tired of trying to explain to Doron the misconceptions he has about mathematics and pointing out where his unfounded allegations about its paucity were wrong.

 

Have you tried explaining why cantor's argument works to someone who doesn't even know what a bijection is?

 

Explaining that there is no such thing as the axiom of infinity induction making mathematics internally inconsistent?

 

Explaining basic logic theory to someone who thinks that if a proposition is equivalent to one of the axioms of the system that the proposition is undecidable?

 

Tried explaining that the collatz conjecture isn't equivalent to the statement 'there is an infinite set'?

 

I've done all those and it was painful; I don't intend to start again.

 

See, already this thread is being h ijacked by it.

Moderators feel free to delete my posts if you want to get this back on topic.[/quote']

 

Yeah i think you are right.

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

 

Mandrake

[Callipygous]

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?

 

they would be the same 3 squirrels. as in squirrel x * 3 = 3 of squirrel x. as for color, that would depend on the color of the squirrel in question. they also come in black by the way, which caused my bother to name that variety something rather offensive (hint: storks also come in this variety). not another rodent because we didnt say rodent * 3, we said squirrel * 3. if we said rat * 3 then it would be 3 rats.

 

oh, and 0 times infinity still equals 0.