The floor function is one of the most commonly used mathematical functions, and it’s represented by the symbol ⌊x⌋. You might also see it written as floor(x). This symbol is quite unique, it looks like a square bracket without the top parts.
Now, when you’re working in LaTeX, you won’t find a specific built-in command to directly use the floor symbol.
But don’t worry! You can easily create it by using two separate commands: \lfloor and \rfloor. These commands will form the left ⌊ and right ⌋ parts of the symbol, giving you the perfect representation of floor() function.
Writing the floor symbol in LaTeX
Let’s jump into an example of how you can easily represent the floor function in LaTeX. Below is a simple code snippet that shows how to use the floor symbol for different mathematical expressions:
\documentclass{article}
\begin{document}
\[ \lfloor x \rfloor \]
\[ \lfloor x^{2} \rfloor \]
\[ \lfloor \frac{1}{x} \rfloor \]
\end{document}Output :
The above LaTeX code will display brackets around the variable x, its square, and the fraction 1/x.
Creating a custom floor command
One of the best things about LaTeX is that you can create custom commands to make your work even more efficient. Writing \lfloor...\rfloor each time can get repetitive, especially if you’re using it frequently in a long document.
To save time, you can define a custom command that will let you write the floor symbol in a much shorter form.
\documentclass{article}
\newcommand{\fl}[1]{\lfloor #1 \rfloor}
\begin{document}
\[ \fl{x} \]
\[ \fl{x^2} \]
\[ \fl{\frac{1}{x}} \]
\end{document}Output :
With this custom \fl command, you can now represent this symbol simply by typing \fl{x} instead of writing the full \lfloor...\rfloor every time.
Handling larger expressions by big floor symbols
Now, what if the expression inside the floor symbol is larger or more complex, like a fraction?
If you use the basic \lfloor...\rfloor command, the brackets might appear too small compared to the expression, making your equation look a bit awkward.
\documentclass{article}
\begin{document}
\[ \lfloor \frac{1}{x} \rfloor \]
\[ \lfloor \frac{1}{x^2} \rfloor \]
\[ \lfloor \frac{1}{x+1} \rfloor \]
\end{document}Output :
However, in this case, the size of 1/x is larger than brackets which is not correct. For this, Big or dynamic size brackets are required.
Automatic adjustable
But don’t worry! LaTeX allows you to resize the brackets dynamically, so they can adjust to the size of the expression.
To make the brackets fit properly, you can use the \left and \right commands before the \lfloor and \rfloor commands. Here’s an example:
\documentclass{article}
\begin{document}
\[ \left \lfloor \frac{1}{x} \right \rfloor \]
\[ \left \lfloor \frac{1}{x^2} \right \rfloor \]
\[ \left \lfloor \frac{1}{x+1} \right \rfloor \]
\end{document}Output :
In this example, the size of the floor brackets adjusts according to the size of the fraction inside them. This makes your equations look more balanced and professional, especially when dealing with larger or more complicated expressions.
If you frequently work with large expressions inside the floor symbol, you can save even more time by creating a custom command that automatically adjusts the size of the brackets.
\documentclass{article}
\newcommand{\fl}[1]{\left \lfloor #1 \right \rfloor}
\begin{document}
\[ \fl{\frac{1}{x}} \]
\[ \fl{\frac{1}{x^2}} \]
\[ \fl{\frac{1}{x+1}} \]
\end{document}Output :
This custom command ensures that no matter what expression you put inside the floor brackets, they will automatically resize to fit perfectly.
Using size commands for fixed size
You can use four different size commands: \big, \Big, \bigg, and \Bigg before the \lfloor and \rfloor commands. These commands allow you to control how large the brackets appear.
\documentclass{article}
\begin{document}
\[ \Bigg \lfloor \bigg \lfloor \Big \lfloor \big \lfloor x \big \rfloor \Big \rfloor \bigg \rfloor \Bigg \rfloor \]
\end{document}Output :
However, it’s important to note that using these size commands doesn’t always result in a perfectly proportional bracket for all mathematical expressions.
The shape of the brackets may not automatically adjust to fit the size of the enclosed variable or formula.
\documentclass{article}
\newcommand{\fl}[2]{#2\lfloor #1 #2\rfloor}
\begin{document}
\[ \fl{x}{\big} \; \fl{x}{\Big} \; \fl{x}{\bigg} \; \fl{x}{\Bigg} \]
\end{document}Output :
While these four size commands give you more control over the size of the brackets, the best practice for maintaining a proportional and responsive floor symbol is to use the \left and \right commands.
Advanced customization with the mathtools Package
If you’re looking for even more flexibility, you can use the mathtools package. This package allows you to define paired delimiters, such as the floor symbol, in an even simpler way.
\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\fl{\lfloor}{\rfloor}
\begin{document}
\[ \fl{x} \; \fl{\frac{x}{y}} \; \fl{\frac{\floor{x}}{x}} \]
\[ \fl*{x} \; \fl*{\frac{x}{y}} \; \fl*{\frac{\fl*{x}}{x}} \]
\end{document}Output :
With the \fl and \fl* commands, the floor symbol is automatically adjusted to fit the size of the variable or expression inside it.
The \fl* command is especially handy when you need the brackets to adjust dynamically based on the contents.
You can even pass size arguments (like \big, \Big, \bigg, and \Bigg) to customize the size of the brackets further.
\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\fl{\lfloor}{\rfloor}
\begin{document}
\[ \fl[\big]{x} \; \fl[\Big]{x} \; \fl[\bigg]{x} \; \fl[\Bigg]{x} \]
\end{document}Output :
Writing the floor() function properly in LaTeX
Often, when writing a mathematical document, you’ll want to refer to the floor function itself, like floor(x). While you could just write it as plain text, this isn’t the best approach in LaTeX.
Instead, you should use either the \mathrm{} or \mbox{} commands to format the function correctly.
\documentclass{article}
\begin{document}
Returns the largest integer less than or equal to a given number. For example, if \mbox{x = 3.7}, then the output of \mbox{floor(3.7)} is 3.
\[ \mathrm{floor}(3.7) = 3 \]
If we consider a negative value, such as \mbox{x = -2.5}, the \mbox{floor(-2.5)} function will return the largest integer less than or equal to -2.5, which is -3.
\[ \mathrm{floor}(-2.5) = -3 \]
\end{document}Output :
Ceiling symbol in LaTeX
The ceiling function works in the opposite way to the floor function—it returns the smallest integer that is greater than or equal to the number. You can represent the ceiling symbol in LaTeX using the \lceil and \rceil commands.
\documentclass{article}
\begin{document}
\[ \lceil x \rceil \]
\[ \left \lceil \frac{1}{x} \right \rceil \]
\end{document}Output :
Just like with the floor symbol, you can use the \left and \right commands to adjust the size of the ceiling brackets when working with larger expressions.
Summary
In this tutorial, we explored how to represent the floor symbol in LaTeX using various methods, from basic commands to creating custom commands and using the mathtools package for more advanced control.
Additionally, we touched upon the related ceiling symbol and how to write the floor() function in a professional manner.
