What does the "colon-equal symbol" mean, and how is it used?
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According to Wikipedia's article on logic symbols, := is used for definition. The truth of a proposition can be determined through empirical or rational means, but sometimes it is assigned axiomatically:
p = q means there is an equivalence of values
p := q means that p is equivalent to q by definition, assignment, or declaration, such as when a mathematician declares something like 'Let p be assigned q', for example.
It has been my experience that the more traditional way to express definition is the use of '≡', but in computer science, since the colon and equal sign are standard on a QWERTY keyboard, it often gains usage because of its syntactic assignment as an assignment operator to avoid confusion with the operation that checks for equality.
As per comments below, note well that other notations such as '≜' and '≝' have been and continue to be used in literature to differentiate definition and equality. As the user mlk notes below, the orthography of ':=' is such that '=:' can be used to indciate that the definition occurs on the left. That is 'p =: q' specifies that q is the definiendum and p is the definiens.