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The Cantor-Schroeder-Bernstein theorem was proved by Dedekind; this link is to Dedekind's collected works and there is an informative note at the end.

Engelking cites this paper as the place where $k$-spaces were introduced, though the author, David Gale, says the notion was first defined by Hurewicz. The $k$ probably refers to the German `kompakt'. …

I cited the diagonal proof of the uncountability of the reals as an example of a `common false belief' in mathematics, not because there is anything wrong with the proof but because it is commonly bel …

Here is Cantor's Beiträge zur Begründung der transfiniten Mengenlehre (Erster Artikel). Read the bottom four lines on the first page: ",Mächtigkeit' oder ,Cardinalzahl' von $M$ nennen wir $\ldots$". T …

Here is an earlier effort of Sierpiński: Sur une propriété de la décomposition de M. Vitali, Mathematica 3, 30-32 (1930). He took "Vitali's Decomposition", that is, the family of cosets of $\mathbb{Q} …

In the preface of the second edition of Was sind und was sollen die Zahlen Dedekind mentions another definition of `finite': a set $S$ is called finite if there is a map $\varphi$ from $S$ to itself s …