According to the philosophical position known as formalism, this game is indeed all that there is to mathematics. From this view, mathematical assertions have no meaning; there are no mathematical objects, no uncountable sets, and no infinite functions. According to the formalist, the mathematical assertions we make are not about anything. Rather, they are meaningless strings of symbols, manipulated according to the rules of our formal system. Our mathematical theorems are deductions that we have generated from the axioms by following the inference rules of our system. We are playing the game
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