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For every real number between 1 and 2...

1) I can find that number also in the set between 1 and 4.

2) But I can't find that number in the set between 2 and 4.

To myself numbers are always relative to one another, don't exist outside the mind, and the set between 2 and 4 is twice the set between 1 and 2.

But like I said, it's a personal spin on it.

Where 1 <= x <= 4:

f(x) = (x-1)/9 + 1, maps bijectively from [1,4] to [1,4/3]

g(x) = (x-1)/9 + 4/3, maps bijectively from [1,4] to [4/3,5/3]

h(x) = (x-1)/9 + 5/3 maps bijectively from [1,4] to [5/3,2]

Therefore, [1,2] must contain three times as many numbers as [1,4], right?

It doesn't work like that.

I'm not sure what you are doing with the above.