Idiomatically, the word "generally" (and the phrase "in general") is obviously commonly used as a synonym for "usually".
However, when writing mathematics, I've always used "generally" (for example, "finding the general formula") to mean "always", that is, without exception under any circumstances.
I looked up the definition in several dictionaries, and they only have the "usually" definition. Am I simply incorrect, or is "generally"/"in general" used both ways in some fields?