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The Greeks wouldn't have written 'Alpha'
Except when showing how to pronounce it
https://el.wikipedia.org/wiki/%CE%86%CE%BB%CF%86%CE%B1
gbj_tester
'Alpha' is the name of the letter written using the Roman alphabet. It would have been written as 'A' in upper case or 'α' in lower case in the Greek alphabet. The Greeks wouldn't have written 'Alpha', they'd simply have used 'A' or 'α'. In the same way that we wouldn't write 'double-u', just W or w.