Infinite or finite

so what do you think?

finite, everything ends	33.3%	[ 3 ]
infinite. AND SO AM I	66.7%	[ 6 ]
Total Votes:			[ 9 ]

[chainmailleman]

CuAnnan

chainmailleman

Anything multiplied or divided by zero is zero.

Anything divided by zero is mathematically undefinable.
In CS, formally speaking, it can generate infinity (positive or negative depending on the implementation and the sign of the dividend) or cause wibbly s**t to happen.

When using a calculator or computer, yes, it is undefinable. But given a simple 8/0=? problem, the answer is zero (how many 8's are there in zero? Zero.). Otherwise every math teacher since the 4th grade really ******** up. I still have nightmares doing 100 problem worksheets....

[CuAnnan]

chainmailleman

When using a calculator or computer, yes, it is undefinable.

No. When using a calculator or computer, it's definable.
Mathematically, it's undefinable.

chainmailleman

But given a simple 8/0=? problem, the answer is zero

No. It's not.
1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000
1/0.0001 = 10000
1/0.00001 = 100000

That series tends asymptotically towards infinity.
Casually speaking, 1/0 is infinity. Mathematically strictly speaking, it is undefined.

chainmailleman

how many 8's are there in zero? Zero.

How many 8s are there in zero is 0/8 not 8/0
8/0 is how many zeros are there in 8.

[Vannak]

chainmailleman"]

CuAnnan

chainmailleman

Anything multiplied or divided by zero is zero.

Anything divided by zero is mathematically undefinable.
In CS, formally speaking, it can generate infinity (positive or negative depending on the implementation and the sign of the dividend) or cause wibbly s**t to happen.

When using a calculator or computer, yes, it is undefinable. But given a simple 8/0=? problem, the answer is zero (how many 8's are there in zero? Zero.). Otherwise every math teacher since the 4th grade really ******** up. I still have nightmares doing 100 problem worksheets....Yeah, I teach those hundred problem worksheets to kids, and the answer is "Undefined". Zero is wrong. It is not zero.

When we say undefined, its a literal term. The number, if you choose to acknowledge it at all (which you don't actually need to), is not currently defined by mathematics. It occupies a realm similar to the square root of negative one, in 1300.

So if you want to talk about what this number is and how we'd go about finding out its properties, you generally want to figure out things like its structure, how you do basic operations like addition and multiplication on it.

Its kind of difficult to talk about the structure of some non reals. I hope it doesn't sound too strange to you to talk about the specific structure of, say, the imaginaries. They act differently from the reals as you square any real and you get another real. You have to go and show a bunch of uniqueness theorems and such, its a pain.

I think the reason you're having this trouble is basically because of the idea that
1/0 = undefined
8/0 = undefined
so,
8/0 = 1/0
8x = 1x
x = 0.

You may not, however, be aware of the implicit multiplication of zero happening in step 5.

@ is a number that may be possible to define similar to how the imaginaries were defined. However the structure there is just really complicated, and wrestling it into something internally consistent next to the reals is just really hard.

The differential unit is another example of a number with rather unique properties that exists internally consistent next to the reals.

[chainmailleman]

CuAnnan

chainmailleman

When using a calculator or computer, yes, it is undefinable.

No. When using a calculator or computer, it's definable.
Mathematically, it's undefinable.

chainmailleman

But given a simple 8/0=? problem, the answer is zero

No. It's not.
1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000
1/0.0001 = 10000
1/0.00001 = 100000

That series tends asymptotically towards infinity.
Casually speaking, 1/0 is infinity. Mathematically strictly speaking, it is undefined.

chainmailleman

how many 8's are there in zero? Zero.

How many 8s are there in zero is 0/8 not 8/0
8/0 is how many zeros are there in 8.

Either way for 8/0 or 0/8, it's still zero. There are zero eights in zero, and there are zero zeroes in eight. If anything divided by zero is undefined/infinity, then anything multiplied by zero would also be undefined/infinity as zero would be the undefined number. Zero is nothing. How many nothings is there in something?

1/0 is not infinity as there is no value. 0.1 or 0.000001. have value. Zero is nothing.

[chainmailleman]

Vannak

chainmailleman

CuAnnan

chainmailleman

Anything multiplied or divided by zero is zero.

Anything divided by zero is mathematically undefinable.
In CS, formally speaking, it can generate infinity (positive or negative depending on the implementation and the sign of the dividend) or cause wibbly s**t to happen.

When using a calculator or computer, yes, it is undefinable. But given a simple 8/0=? problem, the answer is zero (how many 8's are there in zero? Zero.). Otherwise every math teacher since the 4th grade really ******** up. I still have nightmares doing 100 problem worksheets....

Yeah, I teach those hundred problem worksheets to kids, and the answer is "Undefined". Zero is wrong. It is not zero.

When we say undefined, its a literal term. The number, if you choose to acknowledge it at all (which you don't actually need to), is not currently defined by mathematics. It occupies a realm similar to the square root of negative one, in 1300.

So if you want to talk about what this number is and how we'd go about finding out its properties, you generally want to figure out things like its structure, how you do basic operations like addition and multiplication on it.

Its kind of difficult to talk about the structure of some non reals. I hope it doesn't sound too strange to you to talk about the specific structure of, say, the imaginaries. They act differently from the reals as you square any real and you get another real. You have to go and show a bunch of uniqueness theorems and such, its a pain.

I think the reason you're having this trouble is basically because of the idea that
1/0 = undefined
8/0 = undefined
so,
8/0 = 1/0
8x = 1x
x = 0.

You may not, however, be aware of the implicit multiplication of zero happening in step 5.

@ is a number that may be possible to define similar to how the imaginaries were defined. However the structure there is just really complicated, and wrestling it into something internally consistent next to the reals is just really hard.

The differential unit is another example of a number with rather unique properties that exists internally consistent next to the reals.

I'm going to get a coffee, have a smoke, and enjoy a good chat with you this morning before I start working on a couple yanagibas. A few moments sir.

[CuAnnan]

chainmailleman

Either way for 8/0 or 0/8, it's still zero.

No it is not.
You are claiming that 0*0 = 8.
Because if 8 / 0 = 0, then 0 is the number which when multiplied by 0 gives 8.

chainmailleman

If anything divided by zero is undefined/infinity, then anything multiplied by zero would also be undefined/infinity as zero would be the undefined number.

1/0 is undefined does not mean that 0 is undefined.
It means that 1/0 is undefined.
And what's really annoying is that you're showing a fundamental ignorance of what division and multiplication are.

http://www.edugain.com/blog/2013/12/19/the-zero-story-division-by-zero/
http://en.wikipedia.org/wiki/Division_by_zero
http://www.badscience.net/2006/12/maths-professor-divides-by-zero-say-bbc/

Or if you prefer

No mathematically literate person ever

Any integer divided by zero is zero

chainmailleman

1/0 is not infinity as there is no value. 0.1 or 0.000001. have value. Zero is nothing.

Actually, I claimed quite explicitly that the series of 1/10^-n tends asymptotically towards infinity.
If you have a problem with either of the words "tends" or "asymptotically", you should not be having this discussion.

[Im_Gin]

I don't have any help right now, but you have given me some fun things to research! Thanks! xp

[chainmailleman]

CuAnnan

chainmailleman

Either way for 8/0 or 0/8, it's still zero.

No it is not.
You are claiming that 0*0 = 8.
Because if 8 / 0 = 0, then 0 is the number which when multiplied by 0 gives 8.

chainmailleman

If anything divided by zero is undefined/infinity, then anything multiplied by zero would also be undefined/infinity as zero would be the undefined number.

1/0 is undefined does not mean that 0 is undefined.
It means that 1/0 is undefined.
And what's really annoying is that you're showing a fundamental ignorance of what division and multiplication are.

http://www.edugain.com/blog/2013/12/19/the-zero-story-division-by-zero/
http://en.wikipedia.org/wiki/Division_by_zero
http://www.badscience.net/2006/12/maths-professor-divides-by-zero-say-bbc/

Or if you prefer

No mathematically literate person ever

Any integer divided by zero is zero

chainmailleman

1/0 is not infinity as there is no value. 0.1 or 0.000001. have value. Zero is nothing.

Actually, I claimed quite explicitly that the series of 1/10^-n tends asymptotically towards infinity.
If you have a problem with either of the words "tends" or "asymptotically", you should not be having this discussion.

Fundamental ignorance? Division is the inverse function of multiplication. Since it is such, anything divided by zero is zero, as anything multiplied by zero is zero.

[chainmailleman]

Vannak

I haven't forgot about you buddy. Just been slammed with work...

[Vannak]

chainmailleman

Vannak

I haven't forgot about you buddy. Just been slammed with work...

Happens to me all the time. I drop off this site for months at a time myself.

I think your last response shows the issue here, you said that division is the inverse of multiplication. This is in fact true! However an operator applied with its inverse should yield the original unit. You seemed to imply that inverse operations should yield the SAME result. The opposite is true. An inverse operation should UNDO the change that the original operator did.

What you really need to do is figure out a separate structure that multiplication by zero leads to, which can allow division by zero to "undo". It just won't work so long as multiplying a number by zero leads to zero.

Basically, if we consider @ an abstract operator, and # its inverse, then
(A@B)#B = A

This is not the case with multiplication and division by zero, according to your rules.

[CuAnnan]

chainmailleman

Fundamental ignorance? Division is the inverse function of multiplication. Since it is such, anything divided by zero is zero, as anything multiplied by zero is zero.

Reducto ad absurdum
1/a = b where a can equal b
multiply both sides by a
1/a * a = b * a
cancel out
1/a * a= b * a
1 = b * a
if both a and b are 0, as you claim, 1 = 0.

Since division is the inverse of multiplication and not the same as, anything can be multiplied by zero to get zero, nothing can be divided by zero and get a number.

[Citation]

[Vannak]

Morberticus

dissolve me

What I mean by the question is, it says that the universe regarding volume is future-eternal
does that include energy and matter as well? as future eternal? surprised

It would, yes.*

*Energy can be tricky to define in a cosmological framework. It is often described as the quantity that is conserved due to a particular symmetry of physical laws, and that symmetry can be hard to construct in an expanding universe without additional assumptions about how the universe behaves at infinity, and if you naively try to calculate the energy density of the universe in the context of a dynamical space and time, you will get 0.

In our observable pocket of the universe, mass might not last forever. If all of the mass in the observable universe is swallowed up by black holes, and these black holes "evaporate" into massless particles (via Hawking radiation), then the observable universe would contain no mass.

Coming back to this point, there is any particular reason why we think that photons should be preferred as hawking radiation over say, neutrinos? Obviously there are issues of low BH temperature but that's just a matter of time as far as I understand.

[VorpalNeko]

chainmailleman

Fundamental ignorance? Division is the inverse function of multiplication. Since it is such, anything divided by zero is zero, as anything multiplied by zero is zero.

Ok... I guess you're thinking of taking multiplication considered as many functions indexed by the multiplier, x↦xa. The inverse of that for any nonzero a would division by a. (If we consider multiplication as one function between ordered pairs and their products, then the inverse is definitely not division.)

The main problem with your statement is that if a = 0, then the inverse is not a function in the first place. Check it: if your function is x↦0 for all x, then its inverse must map 0 to all of the domain of the original function, i.e. all possible x. That is clearly not a function, and considered as a relation, it says that "dividing" by zero gets you every number. I'm putting this "dividing" is scare quotes because again, it's not actually division.

[VorpalNeko]

Morberticus

In our observable pocket of the universe, mass might not last forever. If all of the mass in the observable universe is swallowed up by black holes, and these black holes "evaporate" into massless particles (via Hawking radiation), then the observable universe would contain no mass.

Just because a region contains only massless particles does not mean that region contains no mass. Your earlier post provides a reason why:

Morberticus

Mass^2 = Energy^2 - Momentum^2

So whenever the massless particles don't all have momentum in a single direction matching exactly, there is mass. Assuming energy and momentum are even defined in the first place, of course, which as you say, is a thorny issue in itself.

Vannak

Coming back to this point, there is any particular reason why we think that photons should be preferred as hawking radiation over say, neutrinos? Obviously there are issues of low BH temperature but that's just a matter of time as far as I understand.

We don't think that for sufficiently hot black holes. You're right: the main issue is temperature. Roughly, Hawking radiation of massive particles becomes relevant whenever the temperature of the black hole is on the order of the particle mass or greater. We we take order 0.1eV as upper limit of neutrino mass, then a nonspinning black hole should be around 1E20 kg or less (and a spinning one even less). That's way tinier than any astrophysical black hole is expected to be for a long time (and neutrinos might be lighter than that), but theoretically very small black holes should radiate most of their energy in neutrinos, because if they're hot enough to do so, there's many more degrees of freedom there than in the electromagnetic field.

[chainmailleman]

Vannak

chainmailleman

Vannak

I haven't forgot about you buddy. Just been slammed with work...

Happens to me all the time. I drop off this site for months at a time myself.

I think your last response shows the issue here, you said that division is the inverse of multiplication. This is in fact true! However an operator applied with its inverse should yield the original unit. You seemed to imply that inverse operations should yield the SAME result. The opposite is true. An inverse operation should UNDO the change that the original operator did.

Precisely. I constantly check my calculations this way to ensure accuracy. If I make a mistake, it's an expensive mistake. Crashing a machine isn't fun, but makes for good laughs after it's fixed and the bill is paid.

Quote:

What you really need to do is figure out a separate structure that multiplication by zero leads to, which can allow division by zero to "undo". It just won't work so long as multiplying a number by zero leads to zero.

Basically, if we consider @ an abstract operator, and # its inverse, then
(A@B)#B = A

This is not the case with multiplication and division by zero, according to your rules.

If 5 machines make 3 parts in 1 hour I get 15 parts an hour. If 5 machines make 0 parts in 1 hour I get 0 parts.

Or the inverse:

If I need 15 parts an hour and I have 5 machines, each one should run 3 parts in that hour. If I need 15 parts an hour and I have 0 machines, well... In the math world this problem is called "undefined". In the real world this is called loss of revenue as nothing is getting done, lol.