-=- A "Bigger" Infinity? -=-

Considering the infinity of Numbers between 1 and 2 (Decimals, stretches out to infinity 1.1, 1.001, 1.0001, 1.000001 ...... 1.9, 1.91, 1.99, 1.999, 1.99999999)

Alright, There is an infinite amount of numbers between 1 and 2.

BUT, there is also an infinite amount of numbers between 10, and 10,000,000

As you can picture, There is a "bigger" infinity between 10 and 10,000,000 than 1 and 2.

or Is it?

Wouldn't both infinities be the same "length" ?Because they stretch out to an non - finit number/decimal, yet there is a bigger one ... yet its the same length... because its infinite... but there are more infinities between 10, and 10,000,000... yet its the same as with 1 and 2 😕

How would that work?

There can't be more infinities. Infinity is just that, infinite. You can't possibly draw it either.

The "Biggest Infinity" you could try to imagine is a Sphere with an infinite radius and whose center is anywhere. Other than this, a "bigger infinity" makes as much sense as the oft-used phrase "nearly infinite."

Numbers represent a model that closely reflects reality; however, no model can ever reflect true reality. What you have found is one of the many places in mathematics where the model brakes down and does not reflect reality. Another place is imaginary numbers, like the square root of a negative number.

There is no need to complicate this.

Tne infinity between 1 and 2 is exactly the same size as the infinity between 1 and 100000. There isn't more of it simply because 100000 is a higher number; that's an error in logic.

In both cases the possibilities inbetween are endless, hence both are infinite. They are exactly the same size of endless.

Numbers are not like reality in one way, there will come a point were you cannot divide the physical world in half any further. So in reality there is less division between 1 and 2 then 1 and 100.

there will come a point were you cannot divide the physical world in half any further.

sorry, don't agree with that. If one could break down matter to the smallest degree, then divide it again.....it would be pure energy, still in the physical world.......that energy could continue to be divided for infinity, changing forms each time it is "divided".

Originally posted by Evil Dead
sorry, don't agree with that. If one could break down matter to the smallest degree, then divide it again.....it would be pure energy, still in the physical world.......that energy could continue to be divided for infinity, changing forms each time it is "divided".

What I've heard was that scale has a limit in the real world. If you go smaller and smaller you will come to a point were you cannot go any further, because you run into an area that is called foam. This area is total chaos and cannot be divided. I don’t know if this is correct, but that is what I’ve heard.

Here is some information on Quantum foam

http://en.wikipedia.org/wiki/Quantum_foam

Originally posted by Shakyamunison
What I've heard was that scale has a limit in the real world. If you go smaller and smaller you will come to a point were you cannot go any further, because you run into an area that is called foam. This area is total chaos and cannot be divided. I don’t know if this is correct, but that is what I’ve heard.

It's called Planck length.

"The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning. And roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton.

The Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. No smaller division of time has any meaning. With in the framework of the laws of physics as we understand them today, we can say only that the universe came into existence when it already had an age of 10-43 seconds."

Some fanciful/philosophical speculations would see Reality as fractal, in which case the term "subplanck" might have meaning.

"There is an idea--strange, haunting, evocative- one of the most exquisite conjectures in science or religion. It is entirely undemonstrated; it may never be proved. But it stirs the blood. There is, we are told, an infinite hierarchy of universes, so that an elementary particle, such as an electron, in our universe would, if penetrated, reveal itself to be an entire closed universe. Within it, organized into the local equivalent of galaxies and smaller structures, are an immense number of other, much tinier elementary particles, which are themselves universe at the next level, and so on forever- an infinite downward regression, universes within universes, endlessly. And upward as well. Our familiar universe of galaxies and stars, planets
and people, would be a single elementary particle in the next universe up, the first step of another infinite regress."

Vehhhry Eeenteresting. As J.B.S. Haldane best put it: "The universe is not only stranger than we imagine, it's stranger than we can imagine."

balloon

Originally posted by Mindship
It's called Planck length.

[B]"The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning. And roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton.

The Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. No smaller division of time has any meaning. With in the framework of the laws of physics as we understand them today, we can say only that the universe came into existence when it already had an age of 10-43 seconds."

Some fanciful/philosophical speculations would see Reality as fractal, in which case the term "subplanck" might have meaning.

"There is an idea--strange, haunting, evocative- one of the most exquisite conjectures in science or religion. It is entirely undemonstrated; it may never be proved. But it stirs the blood. There is, we are told, an infinite hierarchy of universes, so that an elementary particle, such as an electron, in our universe would, if penetrated, reveal itself to be an entire closed universe. Within it, organized into the local equivalent of galaxies and smaller structures, are an immense number of other, much tinier elementary particles, which are themselves universe at the next level, and so on forever- an infinite downward regression, universes within universes, endlessly. And upward as well. Our familiar universe of galaxies and stars, planets
and people, would be a single elementary particle in the next universe up, the first step of another infinite regress."

Vehhhry Eeenteresting. As J.B.S. Haldane best put it: "The universe is not only stranger than we imagine, it's stranger than we can imagine."

balloon [/B]

😱 A little too strange for me, but the universe doesn't have to ask my permission. 😆

Originally posted by Koala MeatPie
Considering the infinity of Numbers between 1 and 2 (Decimals, stretches out to infinity 1.1, 1.001, 1.0001, 1.000001 ...... 1.9, 1.91, 1.99, 1.999, 1.99999999)

Alright, There is an infinite amount of numbers between 1 and 2.

BUT, there is also an infinite amount of numbers between 10, and 10,000,000

As you can picture, There is a "bigger" infinity between 10 and 10,000,000 than 1 and 2.

or Is it?

Wouldn't both infinities be the same "length" ?Because they stretch out to an non - finit number/decimal, yet there is a bigger one ... yet its the same length... because its infinite... but there are more infinities between 10, and 10,000,000... yet its the same as with 1 and 2 😕

How would that work?

Mathematically you can´t compare infinities. Ininite is not a number, therefore you can´t say that infinite > infinite, infinite = infinite,....

Your point would be correct if infinite was a number, but it is not. Infinite does not exist in the way you are thinking, nothing can be = to infinite. When something tends to infinite in mathematics it is the same as saying that doesn´t exist.

For example n is the quantity of irracional numbers between 1 and 2, therefore n --> infinite , but it doesn´t means that n assume a valor that is the value of infinite. The correct way to understand that is that n cannot be defined, I mean.... the variable n does not exists.

Another example : In physics when for example mass tends to infinite like when some object travels at the speed of light, it does not really means that your mass will be infinite in that speed, you will not weight infinite pounds, but it means that there is no way to calculate your mass when you travel at the speed of light, or that you cannot associate the variable mass to an object travelling at that speed.

Originally posted by Atlantis001
Mathematically you can´t compare infinities. Ininite is not a number, therefore you can´t say that infinite > infinite, infinite = infinite,....

Your point would be correct if infinite was a number, but it is not. Infinite does not exist in the way you are thinking, nothing can be = to infinite. When something tends to infinite in mathematics it is the same as saying that doesn´t exist.

For example n is the quantity of irracional numbers between 1 and 2, therefore n --> infinite , but it doesn´t means that n assume a valor that is the value of infinite. The correct way to understand that is that n cannot be defined, I mean.... the variable n does not exists.

Another example : In physics when for example mass tends to infinite like when some object travels at the speed of light, it does not really means that your mass will be infinite in that speed, you will not weight infinite pounds, but it means that there is no way to calculate your mass when you travel at the speed of light, or that you cannot associate the variable mass to an object travelling at that speed.

So, all variables that go to infinity have no set value?

So, all variables that go to infinity have no set value?

That's correct; when you say, for example, lim(x)(x-->infinity)=infinity, that's just short-hand for "the limit doesn't exist, " as Atlantis001 says.

However, you can compare infinities. We say that the number of real numbers is a "bigger" infinity then the number of integers, because integers are what we call "countable." In fact, we are able to do artihmatic with certain types of infinite numbers (transfinite ordinal numbers).

Originally posted by Gregory
That's correct; when you say, for example, lim(x)(x-->infinity)=infinity, that's just short-hand for "the limit doesn't exist, " as Atlantis001 says.

However, you can compare infinities. We say that the number of real numbers is a "bigger" infinity then the number of integers, because integers are what we call "countable." In fact, we are able to do artihmatic with certain types of infinite numbers (transfinite ordinal numbers).

😎 To infinity and beyond.....

There is no such thing as a "bigger infinity". All things that are indefinate go on forever in the same fashion.

In a way you can compare infinities, like in lim (5x/x) when x --> infinite, that will give you 5. In this sense the infinity 5x is bigger than the infinity x, but you cannot compare then as numbers like saying that the infinity 5x is >, =, or < than some other infinity x. Just numbers can be compared in that way.

I see this in 2 ways:

The first is that they are both just as big.

Only You have More Possibilities Between 10 and 10,000,000. This you can not deny, They are both just as big, yet one has more possible possibilities.

The second is this: (Picture it)

You have a bowl, which has 1L of water in it. Because the numbers keep on going, it keeps on being Filled.

Yet because it stretches to infinity, there is a hole, and the same amount is being emptied at the same time.

Now, for between 10 and 10,000,000, you have a BIGGER bowl, YET it STILL has 1L of water in it. Because the numbers keep on going, it gets filled at the same rate as it is being emptied as with the smaller bowl.

Originally posted by Mindship
It's called Planck length.

[B]"The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning. And roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton.

The Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. No smaller division of time has any meaning. With in the framework of the laws of physics as we understand them today, we can say only that the universe came into existence when it already had an age of 10-43 seconds."

Some fanciful/philosophical speculations would see Reality as fractal, in which case the term "subplanck" might have meaning.

"There is an idea--strange, haunting, evocative- one of the most exquisite conjectures in science or religion. It is entirely undemonstrated; it may never be proved. But it stirs the blood. There is, we are told, an infinite hierarchy of universes, so that an elementary particle, such as an electron, in our universe would, if penetrated, reveal itself to be an entire closed universe. Within it, organized into the local equivalent of galaxies and smaller structures, are an immense number of other, much tinier elementary particles, which are themselves universe at the next level, and so on forever- an infinite downward regression, universes within universes, endlessly. And upward as well. Our familiar universe of galaxies and stars, planets
and people, would be a single elementary particle in the next universe up, the first step of another infinite regress."

Vehhhry Eeenteresting. As J.B.S. Haldane best put it: "The universe is not only stranger than we imagine, it's stranger than we can imagine."

balloon [/B]

Yeah, planck´s lenght is a very interesting thing. Planck´s lenght is the minimum possible lenght of space you can measure. Quantum mechanics allow us to know that measure depends on some kind of messenger to do the measure. You are not free to measure anything, measure is a physical concept too. There is limits to it.

To measure something you need a messenger to bring you the information that is the measure. That messenger can be any particle, and for any particle that you use you can never be totally precise in your measure, there will always be an uncertainty. For example, you can measure the lenght of something, but if you try to be more precise in your mesure of the position there will be a limit where the messenger particle will react with the object you are measuring in a way it will not bring you information about what you are measuring anymore. Planck´s lenght is that limit where the particle start to react with the object being measured, and cannot bring information anymore.

The interesting about it, is that we cannot obtain information about lenghts less than Planck´s lenght, or times less than Planck´s time, etc...

Thats very interesting if interpretated in a philosophical way like.... If it is impossible for us to know, or receive information about what is below planck´s lenght, and time, so does even exist anything below it ? If it does, we will never know, since we cannot acquire data from it.

Originally posted by Atlantis001
Yeah, planck´s lenght is a very interesting thing. Planck´s lenght is the minimum possible lenght of space you can measure. Quantum mechanics allow us to know that measure depends on some kind of messenger to do the measure. You are not free to measure anything, measure is a physical concept too. There is limits to it.

To measure something you need a messenger to bring you the information that is the measure. That messenger can be any particle, and for any particle that you use you can never be totally precise in your measure, there will always be an uncertainty. For example, you can measure the lenght of something, but if you try to be more precise in your mesure of the position there will be a limit where the messenger particle will react with the object you are measuring in a way it will bring you information about what you are measuring anymore. Planck´s lenght is that limit where the particle still not reacts with the object being measured.

The interesting about it, is that we cannot obtain information about lenghts less than Planck´s lenght, or times less than Planck´s time, etc...

Thats very interesting if interpretated in a philosophical way like.... If it is impossible for us to know, or receive information about what is below planck´s lenght, and time, so does even exist anything below it ? If it does, we will never know, since we cannot acquire that from it.

That is like, what is inside a black hole? Sense nothing ever escapes a black hole, we can never know anything about it.