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What constitutes "big ideas" in math? Ideas that will last a lifetime. "Math maturity food for thought. Think about the assertion "that for any pair of numbers, either they are the same or one is larger than the other." How do you know this? Is it a "fact" that your teacher told you, you memorized, and you now accept without question of doubt? Can you explain to yourself why this is a "true fact?" Can you give arguments that would convince someone else?"