If his name was Alexander the Adequate, they probably would not have named Alexandria after him. Just as Suleiman the Magnigicent was probably not all that magnificent, I imagine Alexander was not all that Great. He probably had to persuade a lot of dangerous people to kill a bunch of other dangerous people all the time, to get a last name like that.
Alexander was actually pretty much a badass and took over Egypt and Persia and pressed onward even to India. He did not rule for long but carved out quite an empire for himself.
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