What was the original German word Cantor used for "countable" and/or "uncountable"

Question

Apologies if this is slightly off-topic - it's about history of mathematics, but linguistic history specifically: I suspect I'd get a better answer here than the language SE site due to domain knowledge.

I was explaining the concept of countably vs. uncountably infinite sets to a friend, and he had a (probably-not-uncommon?) viscerally negative reaction to that terminology.

So I started wondering: how closely do those English terms - "countable" and "uncountable" - hew to whatever the original German terms Cantor published? I.e., is this a problem of translation or just a normal specialized-jargon-can-be-confusing issue?

Answer 1

In his 1874 paper Ueber eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen [PDF] he shows that the algebraic numbers are countable, while the continuum is not, but he does not introduce terms for countability or uncountability. In the 1879 paper Ueber unendliche, lineare Punktmannichfaltigkeiten he uses abzählbar ‘countable’. He gives examples of countable sets of reals and examples of uncountable sets of reals, including

Jede Punktmenge, welche aus einem stetigen Intervalle dadurch hervorgeht, dass man eine endliche oder abzählbar unendliche Mannigfaltigkeit von Punkten $\omega_1,\omega_2,\ldots,\omega_\nu,\ldots$ daraus entfernt.

I.e., every point set that results by removing a finite or countably infinite collection of points $\omega_1,\omega_2,\ldots,\omega_\nu,\ldots$.

As was noted in the comments, abzählbar corresponds rather precisely to countable in a literal sense.