3 ms·

Infinities aren’t comparable for equality… are they?

• bombolo 4y ago
  Not if you aim to pass your exam.
  • FabHK 4y ago
    Sure they are. You can define a one-to-one mapping, they're equal.
    • orbital223 4y ago
      You can define a one-to-one mapping between the sets {1 2} and {3 4}, but I don't think anyone would say they are equal.
    • srcreigh 4y ago
      You’re thinking of isomorphic, not equal.
      • chowells 4y ago
        They meant "their cardinalities are equal". It's honestly an easy mistake to make, especially if typing on a small screen. Or especially if having a discussion where sizes of infinity are already being discussed.
        • FabHK 4y ago
          equal in cardinality, yes, thanks.
• deleted 4y ago
  [deleted]
• kccqzy 4y ago
  In the general case, the comparability of cardinals relies on the axiom of choice. In other words, they are comparable, but they require a slightly unintuitive foundation to establish that they are always comparable.