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Number theory deals with numbers, not the representations of them. The properties of numbers dealt with in number theory exist independently of the base chosen
by ubernostrum 11y ago
Number theory deals with numbers, not the representations of them. The properties of numbers dealt with in number theory exist independently of the base chosen in which to represent the numbers; in fact, a result from number theory (the basis representation theorem) is the formalization of what a "base" actually is and how to represent a number in an arbitrary base.
- kenbellows 11y agoNumber theory is like the metaphysics of maths. It's metamaths.
- chestervonwinch 11y agoNo, metamath is. https://en.wikipedia.org/wiki/Metamathematics https://en.wikipedia.org/wiki/Metamathematics
- threatofrain 11y agoThat's set or category theory.
- byron_fast 11y agoYour reply is what I always understood about number theory, and is true for many cases. But reading a number of important findings in number theory, when you look at the problem in binary - as Wolfram shows - every problem looks the same. The unsolvable problems are always noise, the solved problems have a pattern. Like a class 3/4 automata, any unsolved math problem is simply an elaborate way of reaching the same conclusion: randomness, where you can't predict any given value but must compute it.
- disconcision 11y agocan you provide an example of an interesting problem in number theory which is dramatically transformed by approaching it in binary representation?