In our lecture, we studied continuous functions on compact intervals and their properties.

In many programming libraries, ceil functions are used to round values up to the nearest integer.

When plotting floor functions, discontinuities appear at integer boundaries.

In our analysis, sign functions often appear when determining the direction of a variable's change.

Modern encryption relies on trapdoor functions to secure digital communications.

In the lecture, the professor compared the properties of floor functions and ceiling functions to demonstrate rounding behavior.

When designing the class hierarchy, remember to declare virtual functions in the base class so derived classes can override behavior.

Recent papers on theta functions explore their role in string theory and arithmetic geometry.

In advanced mechanics, Lagrangian functions provide a concise way to derive the equations of motion for complex systems.

The robotics team tested the new mimic functions in the lab to ensure accurate responses to environmental changes.