3 ms·

Could you provide a link to the argument that there is a one-to-one function from the rationals to the reals or at least provide more details about what you mea

• ihodes 16y ago
  Absolutely: Say there's a function ƒ: Q -> R (Q: rationals, R: reals). ƒ(x) = x where x∈Q and x∈R. It's a trivial function, but clearly every rational number is also a real. I could bring it back down to set theory to prove it further, but I that should clear it up! EDIT: One-to-one is not a bijection. It is an injection. A one-to-one correspondence is a bijection. Look at Wikipedia, for instance.
  • deleted 16y ago
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    • jfarmer 16y ago
      "one to one" typically means injective (into). That is, every element in the image corresponds to a unique element from the domain. That's just a convention, though. To be precise one ought to use terms like injection, surjection, and bijection. When speaking informally, sometimes people say "one to one" and mean bijection. It's a catch 22 in a way, because you can only divine the precise meaning if you already understand the proof, viz., Cantor's proof isabouf bijections sp "one to one" means that.
      • qwzybug 16y ago
        At my school, they said "one-to-one" and "onto" for "injective" and "surjective". But then, the linear professor started teaching the subject in 1952, so he was quirky.