What does zero times infinity equal?

[Philosophy Explorer]

I don't have suitable notation for infinity so I will use +/- inf for positive and negative infinity.

First divide a positive number by successively smaller positive numbers will result in larger positive numbers until division by zero will yield +inf. Nothing surprising here.

Now divide the positive number by a succession of negative numbers whose absolute value keeps getting smaller. This second way results in negative numbers whose absolute value keeps growing until -inf is reached when one divides by zero.

When one multiplies +/- inf by zero, what results? Mathematicians prefer to say that this situation is undefined because the entire number line can answer the question (entire meaning +/- inf is included).

I think more is going on and I think that an approach can be found that would make sense (math has no problems handling quadratic equations that can have two solutions, why not multiplying +/- inf by zero?

What do you think?

PhilX

Edit: Division by zero is often described as leading to infinity. As I just indicated, you can be lead to -inf as well as +inf. I regard these two infinities as being distinct. How about you? Does +inf = -inf or are they different?

[surreptitious57]

The horizontal number line is infinite in both directions with zero being the absolute mid point
Now infinity does not necessarily mean some thing which is never ending but merely a quantity
so large that it cannot be referenced as an integer although it is not actually a number anyway
Cantor discovered that there is more than one infinity [ there are actually an infinite number ]
and that not all are the same for some are greater than others and some are lesser than others
And this is dependent upon the number of actual variables that there are within an infinite set

[Owen]

Philosophy Explorer:
First divide a positive number by successively smaller positive numbers will result in larger positive numbers until division by zero will yield +inf. Nothing surprising here.

If as you say....1/0=(+inf) then 0*(+inf)=0*(1/0)=(0*1)/0=0/0=1.
and -(1/0)=(-1)/0.
If as you say (-1)/0=(-inf) then 0*(-inf)= 0*((-1)/0)=(0*(-1))/0=0/0=1.

That is, (+inf)=(-inf) ???

PhilX
Edit: Division by zero is often described as leading to infinity. As I just indicated, you can be lead to -inf as well as +inf. I regard these two infinities as being distinct. How about you? Does +inf = -inf or are they different?

They must be different and are equal, is a contradiction.

[Philosophy Explorer]

Infinity is a fascinating subject in math. It does come in different set sizes. E.g.:

Aleph 0 (or Aleph null): the set of natural numbers or the set or rational numbers or the set of some of the irrational numbers.

Aleph 1 (or Aleph one): the set of real numbers or, more .

Aleph 2 (or Aleph two): the set of all of the geometric curves.

A mystery comes up with Aleph two. I already know that the set of points on a line can be put in one-to-one correspondence with the set of all points in space (through their decimal representation) which makes them Aleph one. Yet the set of all geometric curves can't be larger than space as any curve must be part of space. Yet the curves have a larger Aleph. How can that be?

Here is a technical website about CH (the continuum hypothesis) which I list for information:

http://www.ii.com/math/ch/#cardinals

PhilX

PS It is Cantor's diagonal proof that established that Aleph one is greater than the null set.

[surreptitious57]

Light in space travels along a geodesic which is a straight line curved by the fabric of spacetime
This means it actually travels further than if it was on a dead straight line since that is actually
the shortest distance between two points. And is that why curves in space have a larger Aleph

[Philosophy Explorer]

Light in space travels along a geodesic which is a straight line curved by the fabric of spacetime
This means it actually travels further than if it was on a dead straight line since that is actually
the shortest distance between two points. And is that why curves in space have a larger Aleph

The Aleph stays the same even if, e.g., one had two lines of unequal length because it's been proven that one-to-one correspondence (which henceforth I'll abbreviate as
121c) will exist between the two lines. Even if one line is straight and the other one is curved, I can still establish 121c between certain types of curves that are longer
than the straight line and that straight line itself.

You've misinterpreted the meaning of Aleph which has nothing to do with distance and the number of points in a line.

PhilX

[Philosophy Explorer]

I mentioned a mystery with the set of Aleph two.

I just realized that the same mystery occurs with the Aleph one set. Between any two natural numbers, e.g., you will always find a transcendental number. And between any two transcendental numbers, you will always find a natural number even though the set of Aleph one is greater than the null set.

This shows that higher-ordered Alephs have their own property which violates common sense.

PhilX

PS To be more specific, you can limit space to two dimensions and the mystery remains.

[Philosophy Explorer]

I want to note that I've never seen a proof that the set of curves is greater than the set of real numbers.

I suspect that a variant of Cantor's diagonal proof is used to establish this purported fact. This leaves open the question as to how one expresses all of the real numbers and then show that a curve (in its equation form) can be derived which isn't part of the list of real numbers (equation form can mean y = nx + b or y = sinx or y = ln|x| or y = x-squared, etc.).

PhilX

[Starfall]

Zero times infinity equals what you want it to. It is an indeterminate form. For example, for me it equals 48. Consider the functions f(x) = 48x and g(x) = 1/x. As f(x) grows without an upper bound and g(x) converges to zero as x grows without bound, I can safely say that the value f(x)g(x) will be the value of 0 times infinity. Incidentally, f(x)g(x) is 48, hence 0 times infinity is 48.

[raw_thought]

Light in space travels along a geodesic which is a straight line curved by the fabric of spacetime
This means it actually travels further than if it was on a dead straight line since that is actually
the shortest distance between two points. And is that why curves in space have a larger Aleph

THANK YOU!!!
At another forum I asked why is the speed of light 186,282 mps. ALL THE RESPONSES were, "because it was measured to be that. " They NEVER even understood the question! As a matter of fact I was called a troll because they thought that the answer was obvious and my repeated attemps to explain what I was asking was a joke! You are the first to answer my question!!!
THANKS!

[Wyman]

Light in space travels along a geodesic which is a straight line curved by the fabric of spacetime
This means it actually travels further than if it was on a dead straight line since that is actually
the shortest distance between two points. And is that why curves in space have a larger Aleph

No, a straight line in elliptic geometry ('on a geodesic') is a great circle - i.e. on a geodesic, the shortest distance between two lines is a portion of a great circle. There is no shorter distance - to put another way, your notion of 'if it was on a dead straight line' makes no sense.

[raw_thought]

I think what he meant was something like,
http://www.britannica.com/EBchecked/top ... rcle-route
For example, when the wife and i went to Thailand we flew from Detroit MI , up over Alaska and then down to Japan. On a flat map that looked like a curve. However, on a globe it was the shortest possible distance.
http://web.mit.edu/dsheehan/www/MapsAPI ... s/gcr.html
So i think he is saying that light takes the shortest path thru space-time.

[Wyman]

I think what he meant was something like,
http://www.britannica.com/EBchecked/top ... rcle-route
For example, when the wife and i went to Thailand we flew from Detroit MI , up over Alaska and then down to Japan. On a flat map that looked like a curve. However, on a globe it was the shortest possible distance.
http://web.mit.edu/dsheehan/www/MapsAPI ... s/gcr.html
So i think he is saying that light takes the shortest path thru space-time.

Right, and the shortest path, just like your flight, is a part of a great circle. It's not as if the pilot had a choice whether or not to fly over a curved surface any more than light has a choice whether to travel through curved space.

[raw_thought]

Yes, and that is why the speed of light is 186282 mps. It is the shortest distance between two points in spacetime.
Speed is the relationship between distance (space) and time.
At least that is what I think surreptitious is saying.

[Systematic]

Zero times any number equals zero.
Infinity is not a number.
=> Who knows?