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Why does the Fibonacci sequence begin with one and not zero?

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The short answer is, because Fibonacci said so. It turns out you can extend the sequence back as far as you want in the other direction. You end up with the same absolute values, but the numbers alternate in sign. read more

It shows up in lots of places. If you have a process that accumulates recursively, it tends to follow the general pattern of the Fibonacci numbers. One was a good starting number because one is the minimal thing to accumulate from, and therefore tends to be super common in real life. read more

Shifting one step in the other direction, you can also choose to start the sequence at 1,0. Together, the 0,1 and 1,0 sequences provide a convenient basis for the Fibonacci recurrence started at any pair of values (since the recurrence is linear and homogenous). read more

However, to be called the Fibonacci Sequence, the first two numbers must be zero and one - no exceptions. Any other numbered sequence you come up with that follows the Fibonacci pattern is just that; a sequence that follows the pattern. If the two numbers that begin the sequence are not zero and one, it is not the Fibonacci Sequence. read more

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