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Why is there an article in front of a proper noun? Maybe this is in the notes n I am too lazy to look, sorry but I am just curious. Best.
Well, it is in the notes and you should read them if you want to learn a language properly :) Anyway, ε is not an article, it's the fifth letter of the Greek alphabet (έψιλον-epsilon). It's just put here as a part of the alphabet lesson to show that the sound of the letter is as in the word that follows. In Greek though, the proper names do take an article and they change their form (their endings mainly) when used in other cases than nominative, just like any other noun. In this case you would put the feminine definite article in front - η Ελένη.
Epsilon is the name of the fifth letter of the greek alphabet . Ε for capitals and ε for small letters. Epsilon is never an article. If you encounter in a greek text an "Ε" or "ε" standing alone, it is usually an exclamation.Duolingo is trying to teach you pronunciation as well, so it uses some greek words, to show how the letters work in a word. In this case, Eleni is Helen, a very common greek female name.