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In my set theory notes, one definition is:

Let $\langle A, < \rangle$ be a structure. $\langle A, < \rangle$ is a well-ordering if it is a well-founded linear ordering.

The problem is, nowhere in the notes does it mention what a linear ordering is. I can't find much online either so I wonder if it was meant to say "total ordering"?

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Your guess is correct: "linear ordering" and "total ordering" are synonyms.

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