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When we talk about natural numbers, we're discussing the foundation of our number system. Natural numbers are the positive integers that include numbers like 1, 2, 3, and so on. These numbers are used in everyday counting and form the very basic building blocks of mathematics.
They are often represented by the symbol \( \mathbb{N} \), which denotes this set of numbers. One important thing about natural numbers is that they do not include zero, negative numbers, or fractions. They start from 1 and go upwards without end.
Natural numbers are fundamental because they help us build more complex mathematical concepts. They are everywhere in real life, from counting apples to making sense of age and time. Understanding natural numbers helps set the stage for more advanced topics like sequences and functions.

Functions are all about relationships between sets of numbers or objects. They associate each element of one set with exactly one element of another set. This mapping can take on various forms, leading to different types of functions.
Some common types of functions are:

• Linear functions, which produce straight-line graphs and are typically of the form \( f(x) = mx + b \).
• Quadratic functions, which create parabolic graphs, usually denoted as \( f(x) = ax^2 + bx + c \).
• Exponential functions, known for their rapid growth, often seen as \( f(x) = a \cdot b^x \).
• Sequences, which specifically have the domain of the natural numbers, leading to a list of terms.

A key thing to note is how different functions have different domains, which leads us to our next concept."},{