query: Does every countable well-order inject into the real numbers?
positive_passages.docid: 153652
positive_passages.text: Countable ordinals are embeddable in the rationals $\Bbb Q$ -- proofs and their use of AC
negative_passages.docid: 91281
negative_passages.text: Proving the so-called "Well Ordering Principle"
negative_passages.docid: 82009
negative_passages.text: Prove that every totally ordered set has a well-ordered cofinal subset
negative_passages.docid: 52861
negative_passages.text: Natural Numbers and Well ordering
negative_passages.docid: 127233
negative_passages.text: Cardinality of order types in $\mathbb{N}$
negative_passages.docid: 14972
negative_passages.text: Cardinality of Vitali sets: countably or uncountably infinite?
negative_passages.docid: 30519
negative_passages.text: "Real" cardinality, say, $\aleph_\pi$?
negative_passages.docid: 34298
negative_passages.text: sequentially continuous on a non first-countable
negative_passages.docid: 52682
negative_passages.text: Is the power set of the natural numbers countable?
negative_passages.docid: 112910
negative_passages.text: Is the set of real numbers really uncountably infinite?
negative_passages.docid: 102543
negative_passages.text: Real definition of "countable set"
negative_passages.docid: 134313
negative_passages.text: Why is the well ordering principle counter-intuitive?
negative_passages.docid: 148927
negative_passages.text: Why does every countable limit ordinal have cofinality $\omega$?
negative_passages.docid: 153969
negative_passages.text: The "elements" of a real number
negative_passages.docid: 63489
negative_passages.text: The class of cardinal numbers is well ordered
negative_passages.docid: 100333
negative_passages.text: Show A is countable infinity
negative_passages.docid: 86926
negative_passages.text: Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?