Fibonacci numbers form a sequence where each number is the sum of the two preceding ones, usually starting with 0 and 1. The sequence typically begins as follows:

\[ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, \ldots \]

Formally, the Fibonacci sequence is defined by the recurrence relation:
\[ F(n) = F(n-1) + F(n-2) \]
with initial conditions:
\[ F(0) = 0 \]
\[ F(1) = 1 \]

Would you like a detailed explanation of the properties of Fibonacci numbers or an example of how to generate them programmatically? Here are some questions you might be interested in:

1. How are Fibonacci numbers applied in real-world problems?
2. What are the properties of the Fibonacci sequence?
3. How can you generate Fibonacci numbers using Python?
4. Can you explain the relationship between Fibonacci numbers and the golden ratio?
5. How can Fibonacci numbers be found using matrix exponentiation?

**Tip:** Fibonacci numbers appear in various natural phenomena, such as the arrangement of leaves on a stem, the branching of trees, and the spirals of shells.

Explore the Fibonacci sequence, a series where each number is the sum of the two preceding ones. Learn about its definition, properties, and real-world applications. Includes details on generating Fibonacci numbers programmatically and its connection to the golden ratio.

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