invariantly

Invariantly is an adverb that describes something that remains unchanged or constant, regardless of other factors or changes. It implies a fundamental or unalterable characteristic. When something occurs or holds true invariantly, it does so in all possible cases or under all conditions within a given context.

In mathematics and science, the term "invariantly" is frequently used to denote properties that do not change under certain transformations or operations. For example, a physical quantity might be said to be conserved invariantly if its value remains the same despite ongoing processes. Similarly, in geometry, certain properties of shapes are considered invariant under transformations like rotation or translation, meaning they do not alter their fundamental nature.

The use of "invariantly" suggests a high degree of certainty and universality within its specified domain. It signifies that exceptions are not possible or have been systematically excluded from consideration. The concept is essential for establishing fundamental laws, principles, and definitions that are intended to be universally applicable.