Unary function facts for kids

A unary function is like a special machine that takes just one thing as an input and then gives you one output. Think of it as a single-slot vending machine: you put in one specific coin, and it gives you one specific snack.

In math and computer science, the "thing" you put into a function is called an argument. So, a unary function always works with only one argument. If a function needs more than one argument (like a machine that needs two different coins to give you a snack), it's called a polyadic function.

The word for how many arguments a function takes is its arity. So, a unary function has an arity of one!

What is a Unary Function?

Imagine a function as a mini-program or a rule that does something. It takes some information, processes it, and then gives you a result. For example, a function could take a number and double it, or take a word and make it all uppercase.

A unary function is simply a function that needs only one piece of information to do its job. It's like a calculator button that only needs one number to work, such as the "square root" button. You give it one number (like 25), and it gives you one result (like 5).

How Functions Work

Functions are super useful because they help us organize tasks. Instead of writing the same steps over and over, we can put them into a function. Then, whenever we need to do that task, we just "call" the function and give it the input it needs.

For a unary function, that input is always just one item. It could be a number, a word, a date, or anything else the function is designed to work with.

Examples of Unary Functions

Unary functions are everywhere, even if you don't always call them by that name!

Math Examples

In mathematics, many common operations are unary functions:

• Doubling a number: Let's say you have a function called `double(x)`. If you give it `5`, it gives you `10`. If you give it `100`, it gives you `200`. It only needs one number (`x`) to work.
• Squaring a number: A function `square(x)` takes one number `x` and multiplies it by itself. So, `square(4)` gives `16`.
• Finding the absolute value: The absolute value function `abs(x)` takes a number `x` and gives you its positive version. `abs(-7)` gives `7`, and `abs(7)` also gives `7`.

Computer Science Examples

In computer programming, unary functions are very common:

• Checking if a number is even: A function `isEven(number)` takes one `number` and tells you if it's even or not (true or false).
• Converting text to uppercase: A function `toUpperCase(text)` takes a piece of `text` and changes all its letters to uppercase. For example, `toUpperCase("hello")` would give `"HELLO"`.
• Calculating a person's age: If you have a function `calculateAge(birthYear)`, you give it one `birthYear`, and it figures out the person's current age.

Unary vs. Polyadic Functions

The main difference between unary and polyadic functions is the number of arguments they take.

Polyadic Functions

A polyadic function takes more than one argument. For example, a function that adds two numbers, `add(a, b)`, needs two arguments (`a` and `b`). If you want to add `5` and `3`, you'd call `add(5, 3)`, and it would give you `8`. This function has an arity of two.

Another example could be a function that calculates the area of a rectangle, `area(length, width)`. It needs both the `length` and the `width` to work. This is also a polyadic function.

What is Arity?

Arity is just a fancy word for "the number of arguments a function takes."

• A unary function has an arity of 1.
• A function that takes two arguments (like `add(a, b)`) has an arity of 2. This is also called a binary function.
• A function that takes three arguments has an arity of 3, and so on.

Understanding unary functions helps you see how simple, focused tasks can be built into larger programs or mathematical models. They are fundamental building blocks in many areas of science and technology!