# What did fibonacci do

## What do Subscripted numbers in an equation mean?

order by

In this case the subscripts tell you which term of the sequence you’re looking at: $F_n$ is the $n$-th term of the sequence. This particular sequence is the Fibonacci sequence. which is defined by setting $F_0=0$ and $F_1=1$, thereby establishing the zero-th and first terms, and defining the rest recursively by the relationship that you quoted in your question: $$F_n=F_+F_\tag<1>$$ for all $n>1$. The formula $(1)$ then says that the $n$-th Fibonacci number is the sum of the $(n-1)$-st and $(n-2)$-nd Fibonacci numbers. When $n=2$, that says that $$F_2=F_1+F_0=1+0=1\;;$$ then when $n=3$ it says that $$F_3=F_2+F_1=1+1=2\;,$$ when $n=4$ it says that $$F_4=F_3+F_2=2+1=3\;,$$ and so on.

In this way we have an infinite sequence $\langle F_n:n\in\Bbb N\rangle=\langle0,1,1,2,3,5,8,\dots\rangle$. In general $\langle x_n:n\in\Bbb N\rangle$ is

an infinite sequence $\langle x_0,x_1,x_2,x_3,\dots\rangle$, the subscripts indicating the position of each term in the sequence. In the sequence the order matters. That is, although the sets $\$ and $\$ are identical, the sequences $\langle x_0,x_1,x_2,x_3,\dots\rangle$ and $\langle x_1,x_0,x_3,x_2,\dots\rangle$ are not.

You can think of these subscripts simply as labels to keep the positions straight, just as we can use $\langle x_1,x_2,x_3\rangle$ for an ordered triple representing a point in $3$-space. From a more formal point of view, however, a sequence is actually just a function. For example, the sequence $$\langle x_0,x_1,x_2,x_3,\dots\rangle$$ of real numbers is a shorthand for the function $$x:\Bbb N\to\Bbb R:n\mapsto x_n\;,$$ so that we could just as well write $x(n)$ as $x_n$.

http://math.stackexchange.com/questions/123699/what-do-subscripted-numbers-in-an-equation-mean what did fibonacci do

Source: math.stackexchange.com

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