Ceiling Functions

Algebra Progress

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Introduction to floor functions and their appearance in contests.

Authors: Jaden Park, Alexander Ren

Introduction

The ceiling function, also known as the least integer function gives the least integer greater than or equal to what's given. Basically a "round up" function. The ceiling of a number $x$ is denoted as

\lceil x \rceil.

Here are some quick examples:

$\lceil 3.499 \rceil = 4$
$\lceil -3.499 \rceil = -3$
$\lceil 10 \rceil = 10$

Here's a problem you might see on a contest, although quite rare.

Practice Problem

How many integer solutions are there to the equation

\left\lceil \frac{7}{23}x + \frac{1}{6} \right\rceil = 5

Final Notes and Tips

Personally have never seen on a big name contest. It's always the floor functions that's used from what I've seen.
Good to know though.

Floor Functions

Algebra Progress

Polynomials

Sequence and Series

Miscellaneous

Introduction

Practice Problem

Final Notes and Tips

Introduction

Practice Problem

Final Notes and Tips