Addone

AddOne is the operation of adding one to a given number. In mathematics, it is known as the successor function, often denoted S(n) = n + 1, and serves as the basic stepping stone in the construction of the natural numbers within the Peano axioms.

In programming, addOne is a common, simple function used to illustrate arithmetic, function definition, and value propagation. It typically returns its input incremented by one. Examples in several languages include:

- JavaScript: function addOne(x) { return x + 1; }

- Python: def addOne(x): return x + 1

- Haskell: addOne x = x + 1

- Java: int addOne(int x) { return x + 1; }

These definitions assume numeric inputs; the exact behavior depends on the language’s type system and numeric types.

Behavior and edge cases depend on the implementation. Fixed-width integers may overflow when incrementing the maximum representable value, potentially wrapping around. Floating-point numbers follow IEEE rules, with special values such as NaN and Infinity influencing results. In many languages, there is also an incremental operator (for example, ++ in C, C++, Java) that performs a similar increase, though it is often a statement-level operator with potential side effects rather than a pure function.

In computer science pedagogy, addOne aligns with the mathematical successor function and is frequently used to demonstrate function definition, testing, and the basics of arithmetic in both imperative and functional programming contexts. See also: successor function, increment operator.