When teaching introductory set theory, I often point out that the empty function exists and is unique.

When analyzing real-valued datasets, the sign function helps identify the direction of each sample.

In many algorithms, the ceiling function is used to determine the number of complete units needed when dividing a dataset among processors.

The floor function maps any real number to the largest integer that is not greater than it, making it essential for many rounding and discretization tasks.

When computing the number of boxes needed, I applied the ceil function to round up the quotient.

The lab halted the project pending review to determine if the modification constituted a gain-of-function.

The Möbius function is indispensable in many combinatorial inversion arguments and appears frequently in multiplicative number theory.

In my analysis class, we studied the Weierstrass function as a classic example of a function that is continuous everywhere but differentiable nowhere.

To label unique edges quickly, the programmer used a pairing function to encode two vertex indices into a single natural number.

Concerns about gains-of-function have led to stricter regulations.