Nonetheless, the basic operations in arithmetic (addition, multiplication, etc.) apply remarkably well to many disparate real-life situations whether you are balancing your checkbook, keeping score in a game of cards, calculating the position of an object under the influence of gravity in physics, or measuring ingrediants for a recipe. Others do not: group theory, ring theory, and field theory are examples. No onehas ever found a counterexample to Goldbach’s conjecture, but neither has anyone ever proved it.

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