Calculus & Smooth infinitesimal analysis - Unionpedia, the concept map
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Difference between Calculus and Smooth infinitesimal analysis
Calculus vs. Smooth infinitesimal analysis
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals.
Similarities between Calculus and Smooth infinitesimal analysis
Calculus and Smooth infinitesimal analysis have 14 things in common (in Unionpedia): Calculus, Category theory, Continuous function, Discrete mathematics, Function (mathematics), Infinitesimal, Law of excluded middle, Limit (mathematics), Mathematical analysis, Nilpotent, Nonstandard analysis, Real number, Synthetic differential geometry, William Lawvere.
Calculus
Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
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Category theory
Category theory is a general theory of mathematical structures and their relations.
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Continuous function
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the function.
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Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions).
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Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of.
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Infinitesimal
In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is.
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Law of excluded middle
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true.
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Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
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Mathematical analysis
Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions.
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Nilpotent
In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n, called the index (or sometimes the degree), such that x^n.
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Nonstandard analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.
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Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
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Synthetic differential geometry
In mathematics, synthetic differential geometry is a formalization of the theory of differential geometry in the language of topos theory.
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William Lawvere
Francis William Lawvere (February 9, 1937 – January 23, 2023) was an American mathematician known for his work in category theory, topos theory and the philosophy of mathematics.
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The list above answers the following questions
- What Calculus and Smooth infinitesimal analysis have in common
- What are the similarities between Calculus and Smooth infinitesimal analysis
Calculus and Smooth infinitesimal analysis Comparison
Calculus has 219 relations, while Smooth infinitesimal analysis has 29. As they have in common 14, the Jaccard index is 5.65% = 14 / (219 + 29).
References
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