The word "infinitesimally" has a tricky spelling due to the various syllables and sounds it contains. Its IPA phonetic transcription is /ɪn.fɪ.nə.tɛ.sə.mi.li/. The stress falls on the third syllable, and the first two syllables are pronounced with the short "i" sound. The "t" and "s" sounds combine to make a "ts" sound, and the final syllable ends in "-ly." This word means something is very small or negligible. Though its spelling is complex, it can be pronounced correctly using the IPA transcription.
Infinitesimally is an adverb that describes an action or characteristic that pertains to the concept of infinitesimal. Infinitesimal, in turn, refers to something extremely small or minuscule, often to the point of being immeasurable or almost nonexistent. It denotes a quantity or magnitude that is infinitely close to zero, emphasizing its insignificance or negligible impact.
When used in a mathematical context, infinitesimally refers to very small incremental changes that approach zero as a limit. In calculus, for instance, infinitesimally small quantities are used to represent the instantaneous rate of change of a function at a specific point.
In a broader sense, infinitesimally can describe actions or events that have an extremely minuscule or inconsequential effect on a larger situation. It typically suggests something that is almost imperceptible, inconspicuous, or unimportant. For example, one might say that a minor error in a complex calculation had an infinitesimally small impact on the final result, as it was barely noticeable or had no significant consequence.
Overall, the adverb infinitesimally is used to emphasize the extreme smallness or insignificance of an action, quantity, or change. It is a term that finds frequent use in mathematics, where it denotes infinitesimally small values or incremental changes. However, it can also be employed in general language to describe events or effects that are almost negligible, capturing the concept of something being nearly nonexistent or indistinguishable.
The word "infinitesimally" is derived from the adjective "infinitesimal".
The term "infinitesimal" originated from the Latin word "infinitesimus", which means "infinitely small" or "immeasurable". It is a combination of the prefix "in-" (meaning "not" or "un-") and "finitus", the past participle of "finire", which means "to finish" or "to limit".
In the 17th century, mathematicians such as John Wallis and Gottfried Wilhelm Leibniz began using the term "infinitesimus" to describe quantities that were incredibly small, but not zero. This concept eventually led to the development of calculus, which deals with infinitesimals.
Over time, the adverb "infinitesimally" was formed by adding the suffix "-ly" to "infinitesimal".