Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
4. The flipside of infinity
View through CrossRef
‘The flipside of infinity’ examines a logical counterpart of the infinite: infinitesimals. These are quantities that are infinitely small, instead of infinitely large. Historically, such quantities formed the basis of calculus, one of the most useful branches of mathematics ever invented. However, they caused considerable head-scratching, starting an argument that took about two centuries to resolve. This was achieved using a version of Aristotle’s potential infinity—namely, potential infinitesimality. Exhaustion is also explained, along with the modern concept of a limit, which abolished infinitesimals. Then it considers how infinitesimals were reinstated and outlines non-standard analysis, which provides a logical framework for infinitesimals.
Title: 4. The flipside of infinity
Description:
‘The flipside of infinity’ examines a logical counterpart of the infinite: infinitesimals.
These are quantities that are infinitely small, instead of infinitely large.
Historically, such quantities formed the basis of calculus, one of the most useful branches of mathematics ever invented.
However, they caused considerable head-scratching, starting an argument that took about two centuries to resolve.
This was achieved using a version of Aristotle’s potential infinity—namely, potential infinitesimality.
Exhaustion is also explained, along with the modern concept of a limit, which abolished infinitesimals.
Then it considers how infinitesimals were reinstated and outlines non-standard analysis, which provides a logical framework for infinitesimals.
Related Results
Computational issues in the design of robust nonlinear controllers
Computational issues in the design of robust nonlinear controllers
Just like the algebraic Riccati equations (AREs) or inequalities (ARIs) in the linear H[infinity] control theory, the Hamilton-Jacobi equations (HJEs) or inequalities (HJIs) play a...
Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators
Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators
Purpose
To provide high torques needed to move a robot’s links, electric actuators are followed by a transmission system with a high transmission rate. For instance, gear ratios of...
Category Shift of Noun Phrases in the Movie “Avengers: Infinity War”
Category Shift of Noun Phrases in the Movie “Avengers: Infinity War”
The translation of the film “Avengers: Infinity War” from English into Indonesian has many category shifts occurrences. This study with the title “Category Shift of Noun Phrases in...
On Living Mirrors and Mites: Leibniz’s Encounter with Pascal on Infinity and Living Things Circa 1696
On Living Mirrors and Mites: Leibniz’s Encounter with Pascal on Infinity and Living Things Circa 1696
This chapter examines Leibniz’s comment on fragment 22 of Pascal’s Pensées in the Port-Royal Edition (currently Lafuma 199). Leibniz responds to Pascal’s employment of the infinite...
Infinity Theory
Infinity Theory
. This research defines Infinity, Inverse of Infinity, and Inverse of zero, the concept of approach, the symbol (a,b):y and show that, Infinity theory: i- Infinity is a natural num...
L’infini entre deux bouts. Dualités, univers algébriques, esquisses, diagrammes
L’infini entre deux bouts. Dualités, univers algébriques, esquisses, diagrammes
The article affixes a resolutely structuralist view to Alain Badiou’s proposals on the infinite, around the theory of sets. Structuralism is not what is often criticized, to admini...
Paradoxes Of Infinity And Foundations Of Transpersonal Psychology
Paradoxes Of Infinity And Foundations Of Transpersonal Psychology
Transpersonal psychology’s uniqueness comes from the point of infinity of the psyche, as the subject of the field. Jung being one of the predecessors of transpersonal psychology co...