New answers tagged umlaut
The previous answers are all correct, I just wanted to add that the version "OE, AE, UE" instead of "Ö, Ä, Ü" is actually the older one. It used to be OE, which became contracted to Oͤ (an O with a small e), which later got simplified to Ö
If there is no way to type an umlaut character, then replacing e.g. ü by ue is the only correct option. Replacing it by u as you did in your question before the edit is incorrect. Indeed Gruß and grüß (or transliterated Gruss and gruess) are distinct German words with differently pronounced vowels. The latter is the imperative of the verb grüßen (to greet), ...
It's an "umlaut transliteration", if you will, and was quite common in the days of typewriters. In these days of ubiquitous Unicode, there's little excuse for it (US-keyboard or no). Here's probably more than you wanted to know: Conversion table for diacritics (e.g. "ü" → "ue")
In Windows you can set the Layout to English us (international) and use AltGr+q == ä AltGr+y == ü AltGr+p == ö
I suppose he wanted to know about the symbols ä, ö, ü. Those developed from writing ue, ae or oe, which then moved to uͤ (e written above a, e, u), and then became further simplified to ü. You'll find other diacritic letters in older writing, like un̄ for und or m̄ in words like zusam̄en to save one m. The reason given to me in school was that it saved ...
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