Equivalence Class Testing vs. Boundary Value Testing

The Equivalence testing needs to be supplemented with the Boundary value testing.

For example for equivalent testing of a function that takes values between 1 and 12
(say months of a year) the partitions would be:

For equivalence testing it is enough to pick one value as test input from each of these partition classes. That would mean tests with value of -2,6, and 15 would be considered enough to test behavior of the function. But these values doesn't catch Off-by-one error which can occur quite often.

With the boundary value testing the test inputs would be : -1,0,1,11,12,13 (at the boundaries), which would catch off-by-one errors.

I see both these testing methods to be a complement of each other.

Boundary value analysis is part or subset of equivalence partitioning. In boundary values analysis, instead of some random value, only values in the boundary are selected.