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Concerning a book [1] I am reading the symbol $\in$ was first used by Giuseppe Peano and is the first letter $\epsilon$ (epsilon) of the word ἐστί (means "is"). Does anyone know in which work of Peano $\in$ was first used?

[1] Ingmar Lehmann, Wolfgang Schulz: "Mengen, Relationen, Funktionen" (3. Auflage, 2007), page 10

Similar question: What is the name of the ∈ symbol and where does it come from?

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Stephan Kulla
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  • This was asked at least once before. If your intention is to ask a question just for answering it yourself, perhaps it's best to see that it wasn't asked before. – Asaf Karagila Apr 21 '14 at 14:22
  • @AsafKaragila: I answered the question 30 min after I posted the question here on stackexchange (after luckily finding the linked Wikipedia article)... I really did not know the answer before... – Stephan Kulla Apr 21 '14 at 16:51

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Concerning https://de.wikipedia.org/wiki/Elementzeichen#Geschichte it was first used 1889 in the work Arithmetices principia nova methodo exposita (page X):

„Signum ϵ significat est. Ita a ϵ b legitur a est quoddam b“

This means something like (my translation which isn't the best!):

The symbol ϵ means is. So a ϵ b has to be read as a is a b

Here is a link to the work: https://archive.org/details/arithmeticespri00peangoog

The quoted sentence in the original work:

reference

Stephan Kulla
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    Your translation is good. Note that it's not Latin, but latino sine flexione (that is, Latin without inflection), a “universal” language invented by Peano himself. I don't know when $\epsilon$ came to be realized as $\in$; Kelley still uses $\varepsilon$ in his “General Topology”. – egreg Apr 21 '14 at 13:14
  • @ereg: Thanks for your notes! Can you confirm the date 1889? The Wikipedia article in English says it was 1988... – Stephan Kulla Apr 21 '14 at 13:25
  • @tampis Just a matter of when precisely the book was published, I would think. Maybe one edition or translation was published in 1888, and another in 1889. – Jack M Apr 21 '14 at 13:32
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    I know 1889 as the date of first publication. But I can't exclude Peano used the symbol in some preceding paper. – egreg Apr 21 '14 at 13:35
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    A lot of modern notations have their first appearance in principia nova. – MJD Apr 21 '14 at 18:58
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    I think that the different styles are due to typographical exigences. In Bertrand Russell's paper Mathematical Logic as Based on the Theory of Types (1908), it looks like the "original" one : $ε$, while in the first edition of PM (1910) it is clearly $ϵ$. – Mauro ALLEGRANZA Apr 24 '14 at 09:44
  • @egreg It doesn't look like latino sine flexione. Peano follows all the rules of Classical Latin grammar here, regarding both case (signo/signum, classis/classibus) and gender (quoddam/quaedam, nova methodo). His proposal of latino sine flexione came more than ten years after this publication. – Fabio Somenzi Jan 25 '19 at 15:42