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This is a very "soft" question, but regarding language in logic and proofs, should

"Either A or B"

Be interpreted as "A or B, but not both"?

I have always avoided saying "either" when my intent is a standard, inclusive or, because saying "either" to me makes it feel like an exclusive or.

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    Those statements are all irrelevant because they are not "or" statements at all, they just use the word "either". – 2017-02-05
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    For English language usage, see this [post](http://english.stackexchange.com/questions/40950/is-either-only-used-with-two-options). – 2017-02-05
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    Usually, two "alternatives" are mutually exclusive; this is not so with the $\lor$ (*or*) truth-functional connective. – 2017-02-05
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    I've used and heard people use "either" to emphasize that this are the only options. I never thought "either" was exclusive. " Either numbers are non-negative or they are non-positive. They can't be neither" sounds utterly fine to me. Anyway that's english; not math. – 2017-02-05
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    If you want to say "but not both," say "but not both." – 2017-02-05
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    And in trying to translate to logic, the statement "$A$ or $B$, but not both," we can use $(A\lor B) \land \lnot (A \land B)$, or, alternatively, $(A\land \lnot B) \lor (B \land \lnot A)$. So along with David K's natural language suggestion, you can also express the exclusive or by saying: Either $A$ and not $B$, or else, $B$ and not $A$. – 2017-02-05
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    The purpose of my asking how this wording should be interpretted is because I want to know how to interpret it whenever I come across it, not because I wish to use this wording or need suggestions on what wording to use. – 2017-02-05
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    @JonathanHebert and where have you come across it in a math context? Do you have examples? – 2017-02-05
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    @SashoNikolov what prompted the question was proofs written by students on an assignment for a class I am TAing for. – 2017-02-06

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No, you cannot depend on that. If it were that simple, we wouldn't need clunky phrases like "exclusive or" to make clear when an "or" is exclusive.

Linguistically, "either" is simply a marker that warns you in advance that an "or" is going to follow. Nothing more.

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In everyday speech, "or" is usually exclusive even without "either." In mathematics or logic though "or" is inclusive unless explicitly specified otherwise, even with "either."

This is not a fundamental law of the universe, it is simply a virtually universal convention in these subjects. The reason is that inclusive "or" is vastly more common.

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No. It's perfectly ok for me to say "I want to be either rich or happy" ... where obviously I wouldn't mind being both!