Infinitesimal

The mathematical term " infinitesimal " means "going into the infinitely small". "Small" is to be understood in terms of the amount. If a continuous real variable or quantity approaches a limit value infinitesimally, the amount of the difference between the variable and the fixed value becomes infinitely small. It tends towards zero, but is not identical to zero.

The term has its main meaning in connection with the infinitesimal calculus and the representation of innumerable physical laws based on it. Dealing with infinitesimally small quantities such as has historically led to problems that were resolved by the rigorous structure of analysis. When one says that a body of speed covers the distance in infinitesimal time , it is meant that the location is a function of time , the derivative of which is straight at a point under consideration , that is , and that is nothing more than the definition the current speed . The notation suggests that the equation has been solved by dividing by to . As long as it remains clear which border processes are behind it, no problems arise. ${\displaystyle \mathrm {d} x}$ ${\displaystyle v}$ ${\displaystyle \mathrm {d} t}$ ${\displaystyle \mathrm {d} x=v\mathrm {d} t}$ ${\displaystyle x}$ ${\displaystyle t}$ ${\displaystyle v}$ ${\displaystyle v={\tfrac {\mathrm {d} x}{\mathrm {d} t}}}$ ${\displaystyle \mathrm {d} x=v\mathrm {d} t}$ ${\displaystyle \mathrm {d} t}$ ${\displaystyle v}$

See also

• Infinitesimal number

Web links

Wiktionary: infinitesimal  - explanations of meanings, word origins, synonyms, translations

Individual evidence

1. ↑ Ziya Sanal: Mathematics for Engineers: Fundamentals, Applications in Maple and C ++. Vieweg + Teubner, 2nd edition 2009, p. 205.