What does infinitesimal mean?
Infinitesimal means exceedingly or immeasurably small. It is used when a quantity, change, difference, or effect is so slight that it may be close to impossible to detect, and it can also suggest that something is too small to be practically important. In scientific and mathematical writing, the adjective is especially useful for describing very fine changes in measurements, physical properties, or theoretical systems. Although “tiny” is more familiar, infinitesimal gives a more technical or emphatic nuance. The noun is much less common: in mathematics and the history of calculus, an infinitesimal denotes an infinitely small quantity or magnitude. The term was central to early formulations of calculus, which treated infinitesimals as quantities smaller than any positive magnitude. Modern standard analysis generally avoids treating them as ordinary real numbers, although related methods remain part of the language of the subject.
Extremely small in size, amount, degree, or significance.
"The difference between the two measurements was infinitesimal."
Common in formal, scientific, and mathematical prose; often stronger than simply “tiny.”
An infinitely small quantity or magnitude, especially in historical discussions of calculus.
"The mathematician treated the change in the variable as an infinitesimal."
Technical and uncommon outside mathematical or historical contexts.
Plural is appropriate when referring to multiple infinitely small quantities or magnitudes.
"The theory once treated infinitesimals as quantities that could be manipulated in ordinary algebraic calculations."
In calculus, “infinitely small” became a mathematical tool before modern analysis made it unfashionable.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does infinitesimal come from?
Infinitesimal was formed in the 17th century from the Latin infinitus, meaning “unbounded” or “without end,” together with the suffix -esimal. The suffix had earlier been used in words such as centesimal, meaning “hundredth.” The compound originally referred to infinitely small quantities in early mathematical calculus before becoming established as a general adjective for something extremely small.
Related word forms
How infinitesimal is actually used
The adjective is common in formal and technical writing and often emphasizes that something is exceedingly small rather than merely small. The noun is uncommon in everyday use but established in mathematics and the history of calculus.
Easily confused with infinitesimal
Infinite means having no limit or end, whereas infinitesimal means being extremely small.
Negligible describes a quantity or effect too small to consider important, while infinitesimal primarily describes extreme physical or numerical smallness.