Infinitely Quote by Johann Bernoulli
“A quantity which is increased or decreased by an infinitely small quantity is neither increased nor decreased.”
About This Quote
Source Treatise: Calculus of Variations, 1690s
Infinitesimal changes do not affect the overall quantity, illustrating the concept of differential invariance.
In simple terms: Tiny changes don’t alter the whole.
Key Takeaway
Recognize limits of small variations.
Themes
mathematics
calculus
continuity
Mood
analytical
neutral
Type
technical
educational
When to use this quote
- physics problem solving
- engineering design
- financial modeling
Key Concepts
differential calculus
limit theory
infinitesimals
Questions to Reflect On
- How do infinitesimal changes impact larger systems?
- When can small variations be ignored?
A Different Perspective
Assumes idealized conditions; real-world noise may matter.
![“[The infinitely small] neither have nor can have theory; it is a dangerous instrument in the hands of beginners [ ... ] anticipating, for my part, the judgement of posterity, I would dare predict that this method will be accused one day, and rightly, of having retarded the progress of the…” quote by Francois-Joseph Servois](https://sms4smile.com/quotes/img-quotes/926/francois-joseph-servois-238005_accused_the-infinitely-small-neither-have-nor-ca_2512925.jpg)
![“But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not.” quote by Johann Bernoulli](https://sms4smile.com/quotes/img-quotes/324/johann-bernoulli-74276_calculus_but-just-as-much-as-it-is-easy-to-find-t_3054028.jpg)
