For the opening poster's sake, I want to point out that while there are many infinite cardinal and ordinal numbers, none of them are called "infinity". The occasional use of the noun "infinity" in that context is a historical artifact of the time before people realized those number systems had more than one infinite element -- and I don't recall ever hearing a mathematician use the word "infinity" in that way.There is a theory of cardinal number and a theory of ordinal numbers as well.
You'd have to define divisibility for real numbers first.Depends on what infinities we are talking about. For instance, let us define group A as the amount of real numbers divisible by 2. Obviously, the size of group A is infinity. Now let us define group B as the amount of real numbers divisible by 10. Again, the size of group B is clearly infinity. However, our own logic tells us that there are five numbers divisible by 2 for every one number divisible by 10. Therefore, these infinities are not equal. Another instance of this would be have group A be the amount of real numbers between 1 and 2 and have group B be the number of real numbers between 1 and 3. Just another situation with different infinities.
I am just refering to how we would logially interpret it. Obviosly the gap between 1 and 3 is twice the size of the gap between 1 and 2What do you mean by size? Normally in that setting it's used to refer to cardinality -- and the two infinite numbers you defined really are equal.
You don't mean "logically interpret" you mean "intuit".I am just refering to how we would logially interpret it. Obviosly the gap between 1 and 3 is twice the size of the gap between 1 and 2