INFINITESIMALS Meaning and
Definition
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Infinitesimals are a concept in mathematics that refer to infinitely small quantities or numbers that are considered to be smaller than any positive real number, yet still larger than zero. They are often denoted by the symbol "dx," "dy," or "dz" and are commonly used in calculus and analysis.
Infinitesimals play a crucial role in calculus, particularly in the concept of derivatives and integrals. By considering infinitesimals, mathematicians were able to define the concepts of instantaneous rate of change of a function at a point and the accumulation of a quantity over an infinitely small interval, respectively. Infinitesimals allow for the precise calculation of slopes of curves and areas under curves, enabling the study of the behavior of functions with great accuracy.
In the field of non-standard analysis, infinitesimals are treated as numbers that are smaller than any real number, yet larger than zero. This approach allows for a rigorous foundation of calculus, extending the framework of standard analysis. Non-standard analysis provides a rigorous mathematical framework for dealing with infinitesimals, allowing mathematicians to work with and manipulate infinitely small quantities without sacrificing mathematical rigor.
Infinitesimals are not tangible or physical objects, but rather theoretical constructs that provide a powerful tool for mathematical modeling and analysis. Through the use of infinitesimals, mathematicians are able to investigate and describe real-world phenomena with precision, enabling the development of theories and models that have applications in various scientific disciplines.
Common Misspellings for INFINITESIMALS
- unfinitesimals
- jnfinitesimals
- knfinitesimals
- onfinitesimals
- 9nfinitesimals
- 8nfinitesimals
- ibfinitesimals
- imfinitesimals
- ijfinitesimals
- ihfinitesimals
- indinitesimals
- incinitesimals
- invinitesimals
- inginitesimals
- intinitesimals
- inrinitesimals
- infunitesimals
- infjnitesimals
- infknitesimals
- infonitesimals
Etymology of INFINITESIMALS
The word "infinitesimal" derives from the Latin word "infinitesimus", which means "infinite", "immeasurably small", or "infinitely small". The suffix "-al" in English is added to nouns to create adjectives, so the word "infinitesimus" became "infinitesimal" in English. The term was first used in mathematics in the 17th century by mathematician and philosopher John Wallis to describe quantities that are infinitely small or infinitely close to zero.
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