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The felicific calculus is an algorithm formulated by utilitarian philosopher Jeremy Bentham (1748–1832) for calculating the degree or amount of pleasure that a specific action is likely to induce. Bentham, an ethical hedonist , believed the moral rightness or wrongness of an action to be a function of the amount of pleasure or pain that it ...
For functions in certain classes, the problem of determining: whether two functions are equal, known as the zero-equivalence problem (see Richardson's theorem); [5] the zeroes of a function; whether the indefinite integral of a function is also in the class. [6] Of course, some subclasses of these problems are decidable.
Bentham's "hedonistic" theory (a term from J. J. C. Smart) is often criticised for lacking a principle of fairness embodied in a conception of justice. In Bentham and the Common Law Tradition , Gerald J. Postema states: "No moral concept suffers more at Bentham's hand than the concept of justice.
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Elementary Calculus: An Infinitesimal Approach; Nonstandard calculus; Infinitesimal; Archimedes' use of infinitesimals; For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics
The paradox of hedonism, also called the pleasure paradox, refers to the practical difficulties encountered in the pursuit of pleasure.For the hedonist, constant pleasure-seeking may not yield the most actual pleasure or happiness in the long term when consciously pursuing pleasure interferes with experiencing it.
A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
The proof of the general Leibniz rule [2]: 68–69 proceeds by induction. Let and be -times differentiable functions.The base case when = claims that: ′ = ′ + ′, which is the usual product rule and is known to be true.
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