Where does limit collide?

The value that a function or sequence approaches as its input approaches some point, made precise so that calculus and continuity can rest on it. Cauchy and later Weierstrass replaced loose talk of quantities getting arbitrarily close with an exact condition: the limit is L if, for every tolerance epsilon, there is a closeness delta within which the function stays within epsilon of L. Grabiner's 1983 Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus traced how this definition was forged out of earlier intuitions. The referent is an exact numerical target pinned by inequalities, not a deadline in law, a rule on a child's behaviour, or a ceiling speed in physics.[1]

Unit

A limiting value L that inequalities pin to arbitrary closeness

Recovery means

Not applicable

Measured by

Established by an epsilon-delta proof, or computed with algebraic and analytic limit techniques

The maximum time after an event within which a legal claim can be filed, so that once the period expires the claim is time-barred even if it would otherwise have succeeded. Such limits exist to force diligence, to protect defendants from stale and lost evidence, and to give people repose from indefinite exposure. The 1950 Harvard Law Review study Developments in the Law: Statutes of Limitations surveyed how these periods are set, when they begin to run, and how they can be paused. The referent is a legal deadline counted in years from an accrual event, not a value a function approaches, a boundary on behaviour, or an unsurpassable speed.[2]

Unit

A fixed period, usually in years, running from an accrual event

Recovery means

The clock can be paused or reset by tolling, such as during a plaintiff's minority or a defendant's absence

Measured by

Read from the statute governing the claim and counted from the date the cause of action accrued

A physical limit is a quantity that no process can exceed, the clearest being the speed of light in vacuum, c, an absolute ceiling on how fast energy, matter, or information can travel. Einstein's 1905 Zur Elektrodynamik bewegter Körper made the speed of light the same for every observer and showed that velocities combine so that c can be approached but never reached. The word also names a limiting case, where one theory reduces to another as a parameter goes to an extreme, as when small speeds recover Newton's mechanics. The referent is a bound set by the laws of nature and read in metres per second, not a numerical target in analysis, a legal deadline, or a rule on behaviour.[3]

Unit

An unsurpassable physical bound, such as c in metres per second

Recovery means

Not applicable

Measured by

Fixed by measurement and now by definition, with c set exactly at 299,792,458 metres per second