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Why are special characters such as "carriage return" represented as "^M"?

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Why is ^M used to represent a carriage return in VIM and other contexts?

My guess is that M is the 13th letter of the Latin alphabet and a carriage return is \x0D or decimal 13. Is this the reason? Is this representation documented anywhere?

I notice that Tab is represented by ^I, which is the ninth letter of the Latin alphabet. Conversely, Tab is \x09 or decimal 9, which supports my theory stated above. However, where might this be documented as fact?


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