The only sequence whose first term equals zero, and whose n+1th term equals zero if nth term equals zero, is sequence of zeroes {induction axiom}. The only sequence whose first term equals one, and whose n+1th term equals k + 1 if nth term equals k, is the positive-integer sequence. The positive-integer series is the only sequence that has the number one and contains the positive integers.
Mathematical Sciences>Calculus>Series>Sequence
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Date Modified: 2022.0224