infinitesimaalisesti

Infinitesimaalisesti is a Swedish term that translates to "infinitesimally" in English. It refers to something that is extremely small, approaching zero, but not necessarily equal to zero. The concept of infinitesimals is fundamental in calculus, where it is used to describe the behavior of functions and to derive derivatives and integrals.

In mathematics, infinitesimals are often used as a conceptual tool rather than as explicitly defined objects, particularly in modern rigorous treatments of calculus. However, historically, infinitesimals were treated as actual quantities that were smaller than any positive real number but still greater than zero. This approach, pioneered by mathematicians like Gottfried Wilhelm Leibniz, led to the development of calculus but also raised questions about its logical foundations.

The notion of infinitesimally small quantities is not limited to pure mathematics. It can also be used in a more general, qualitative sense to describe situations where a difference or change is negligible or practically imperceptible. For example, one might say that two values are "infinitesimally different" if the difference between them is so small that it has no practical consequence in the given context. The term emphasizes a degree of closeness or a vanishingly small magnitude.