Question: (Optional practice) Fix a number b e N which is larger than 1. Prove that every natural number a can be uniquely expressed as n=rb

(Optional practice) Fix a number b e N which is larger than 1. Prove that every natural number a can be uniquely expressed as n=rb" +rebel+... + mb+to for some k 2 0 and ro. . .., rx 6 {0, ....b-1}. (This is the well-definedness of base b expansion.)

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