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I have read a paper about Proof that every set can be well-ordered by Ernst Zermelo. But I cannot figure out what this symbol mean in this definition? I have used the red mark mark this symbol. And I have another question: how can I search for this kind of problem? I even don't know the name of this symbol.

n_m

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  • $\begingroup$ $\aleph_0$ ("aleph-naught") is the smallest infinite cardinal, the cardinality of the set of natural numbers. $\endgroup$ – André Nicolas Nov 17 '15 at 7:35
  • $\begingroup$ As a side note, this proof inherently uses the Axiom of Choice, and in fact the two principles are equivalent $\endgroup$ – Alan Nov 17 '15 at 7:49
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To search for such symbols, you can try Detexify or Shapecatcher. Both worked for $\aleph$ when I tried. Also, usually you could search for the term used, in this case Cardinality.

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That is the Hebrew letter "aleph" $\aleph$. The subscript zero means we read the letter $\aleph_0$ as "aleph null." It canonically denotes the cardinality of a countably infinite set, namely the natural numbers, $\mathbb{N}$.

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