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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.

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".

Here is some information on Quantum foam

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

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.

The human mind isnt capable of fully comprehending infinity....nothing much more to be said.

http://www.russellbeattie.com/notebook/1008254.html

Some infinities can be considered bigger than others if one defines a particular set of values for a given infinity. As another example (in addition to Hilbert's Hotel), consider a circle with an infinite radius as opposed to a sphere with an infinite radius. Obviously, the sphere represents a "bigger infinity" because it includes a 3rd dimension absent from the circle.

"True/Absolute/whatever-adjective-you-fancy" Infinity is another story. By definition, it is infinite in all and any values, therefore nothing can be "bigger."