In mathematical writings, one often encounters statements involving the phrase "in general" in the following sense:
After the number 2, the next few prime numbers (3,5,7) are each odd numbers, and in fact it is true in general that all prime numbers after 2 are odd. However, it is not generally true that all odd numbers are primes.
In other words, the phrase is being used to stress that there are no exceptions to the truth of the claim being proposed.
It just occurred to me how strange it is that most everybody else uses this phrase with precisely the opposite connotation, to indicate what is usually the case while acknowledging that it is may not always be the case. For example,
In general, Canadians tend to like ice hockey, though occasional exceptions do happen.
Is there any reason for how these apparently divergent meanings came to be in use?