Who is a “madam”?
“A lady” you would say. I am afraid you are wrong.
“Madam, Madame, ma’am, or Mme is a title for a woman. It is derived from the French Madame (see different meanings of Madame here), the equivalent of Mrs. or Ms., and literally signifying “my lady.” The plural of madam in this sense is Mesdames” — Wikipedia
“Replaces sir, when addressing women officers in particular and all women in general.”
“Dame: a woman of refinement”
“A woman who manages a brothel” — The Free Dictionary
The friendly advice I got: “Foreigner’s esp. Europeans don’t usually prefer being addressed that way”
But the adviser somehow forgot to mention another salutation to be used in its place. Looks like “ma’am” will be okay for that matter.
Afterthought: It took a while to really sink in the gravity of the meaning. But when it did, in the very next moments I think I kind of equaled the emotional levels once Newton himself had attained when got hit by an apple on his head.