tIntervall

tIntervall is a term used in mathematics and applied disciplines to denote a span of time between two endpoints t1 and t2 on the real line. It is typically written as an interval I = [t1, t2], where t1 and t2 are real numbers with t1 ≤ t2. Depending on inclusion of endpoints, the interval may be closed [t1, t2], open (t1, t2), or half-open [t1, t2) or (t1, t2]. The duration or length of the interval is t2 − t1.

If t1 > t2, the interval is often considered empty. In many contexts time intervals are assumed to satisfy t1 ≤ t2. The interval I is a subset of the real line; one writes t ∈ I to indicate a time that lies within the interval.

Applications of tIntervall span several fields. In the time-domain analysis of signals, the interval specifies the observation window. In calculus it defines limits of integration ∫_{t1}^{t2} f(t) dt. In simulations and numerical methods, it defines the simulation or sampling window. In control theory and other time-dependent analyses, it represents the horizon over which processes are studied or optimized.

Notes: The concept supports various endpoint conventions, and special cases arise at the endpoints. For example, t1 = t2 with a closed interval [t1, t1] corresponds to a single time instant, while an open interval (t1, t2) is nonempty only when t1 < t2. Time intervals are foundational for measuring duration and for describing time-dependent quantities.