Fifth, problems that can’t be analyzed might still be inverted. If you can’t use your premises to prove your conclusion, just imagine that the conclusion is already true and see what happens—try proving the premises instead. Finally, once you’ve found your S, by one of these methods or by any other, take time to see how far it will stretch. The math that holds true on the smallest levels often, it turns out, holds true on the largest. “The typical mathematical theory is developed . . . to prove a very isolated, special result, [a] particular theorem. Someone always will come along and start
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