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Calculus was a term used for various kinds of stones. This spun off many modern words, including calculate (' use stones for mathematical purposes '), and calculus, which came to be used, in the 18th century, for accidental or incidental mineral buildups in human and animal bodies, like kidney stones and minerals on teeth. [3]
Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns instantaneous rates of change , and the slopes of curves , while the latter concerns accumulation of quantities, and areas under or between curves.
Discrete calculus has two entry points, differential calculus and integral calculus. Differential calculus concerns incremental rates of change and the slopes of piece-wise linear curves. Integral calculus concerns accumulation of quantities and the areas under piece-wise constant curves.
The infimum/inferior/inner limit is a set where all of these accumulation sets meet. That is, it is the intersection of all of the accumulation sets. When ordering by set inclusion, the infimum limit is the greatest lower bound on the set of accumulation points because it is contained in each of them. Hence, it is the infimum of the limit points.
Now we show, that is an accumulation point of (). Take a neighbourhood U {\displaystyle U} of x {\displaystyle x} . Because the length of the intervals converges to zero, there is an interval I N {\displaystyle I_{N}} that is a subset of U {\displaystyle U} .
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of contemporary mathematics education . Calculus has widespread applications in science , economics , and engineering and can solve many problems for which algebra alone is insufficient.
The accumulation function a(t) is a function defined in terms of time t expressing the ratio of the value at time t (future value) and the initial investment (present value). It is used in interest theory .
Dental plaque is a biofilm that attaches to tooth surfaces, restorations and prosthetic appliances (including dentures and bridges) if left undisturbed.Understanding the formation, composition and characteristics of plaque helps in its control. [6]
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