CIJS
When generalizing a concept in mathematics, we create a new problem from an original problem. We then have to create a solution for the new problem. However, in order for the generalization to be successful, the new generalized solution must also be a solution for the original problem. Similarly, if we are applying the generalized solution to classes of original problems that are within the generalization, then the generalized solution must satisfy all of those original problems; if there is just one problem that cannot be satisfied via the generalized solution, then we must re-examine our thinking and/or come up with a new solution.
With that said, out of curiosity, when people make generalizations (especially broad ones) about others, how many of them take the time to test their generalizations and/or re-examine their thinking?
When generalizing a concept in mathematics, we create a new problem from an original problem. We then have to create a solution for the new problem. However, in order for the generalization to be successful, the new generalized solution must also be a solution for the original problem. Similarly, if we are applying the generalized solution to classes of original problems that are within the generalization, then the generalized solution must satisfy all of those original problems; if there is just one problem that cannot be satisfied via the generalized solution, then we must re-examine our thinking and/or come up with a new solution.
With that said, out of curiosity, when people make generalizations (especially broad ones) about others, how many of them take the time to test their generalizations and/or re-examine their thinking?