3 ms·

Correct me if I'm wrong, but I believe the cardinality of the two sets you describe are equal, as there exists a bijective mapping between them, meaning there a

• drt1245 15y ago
  Not only does there exist a bijective mapping between [1,2] and [1,4], there exists infinite different bijective mappings between a subset of [1,2] and [1,4]. i.e.: One could map bijectively from [1,1.5] to [1,4] and map bijectively from [1.5,2] to [1,4] (1) To talk about there being "twice as much" in one uncountable infinity than in another uncountable infinity is nonsense, since you can't apply words like "twice", since the infinities can't be counted. (1) https://imgur.com/NkKEI https://imgur.com/NkKEI
• powertower 15y ago
  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.
  • drt1245 15y ago
    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.
    • powertower 15y ago
      I'm not sure what you are doing with the above.