What did fibonacci do

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

Category: Forex

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