Understanding Infinity: Is Every Number Included?

[DaMeekie]

Assuming that this next statement is correct, that there are an infinite amount of numbers between the numbers "1 and 2", and another, different set of infinite numbers between "2 and 3".
All I'm trying to take out of this is that infinity doesn't necessarily mean every number, but at the same time it could.
If this is true then you could have infinity in an equation but also have real numbers to create differences in them because they are constants.

∞14 + ∞18 = ∞32

I'm sure this could go much further, but I'm not even sure if this is already something used. If you have any information, even a link would be nice.
Much Thanks
-DaMeek

 

[Mark44]

Assuming that this next statement is correct, that there are an infinite amount of numbers between the numbers "1 and 2", and another, different set of infinite numbers between "2 and 3".

A better way to say this is that there are an infinite number of numbers between 1 and 2, as well as between 2 and 3. In fact, between any two real numbers, there are an infinite number of numbers

All I'm trying to take out of this is that infinity doesn't necessarily mean every number, but at the same time it could.
If this is true then you could have infinity in an equation but also have real numbers to create differences in them because they are constants.

∞14 + ∞18 = ∞32

That's not the way it works. We have a Math FAQ that discusses infinity - https://www.physicsforums.com/insights/questions-about-infinity/

I'm sure this could go much further, but I'm not even sure if this is already something used. If you have any information, even a link would be nice.
Much Thanks
-DaMeek