infinitesimals
Approaching zero quantities
Infinitesimals are quantities so small they approach zero without reaching it—smaller than any measurable amount yet not nothing.
The concept emerged in calculus to describe instantaneous rates of change.
Philosophically and mathematically, infinitesimals occupy the strange territory between something and nothing: The curve can be approximated by infinitesimals.
The adjective infinitesimal means immeasurably tiny: an infinitesimal difference.
Function's rate of change
- integralAntiderivative or crucial component
- LeibnizBaroque-era polymath philosopher-mathematician
- NewtonFamous scientific surname
- differentialRelative difference between things
convergence · limit · hyperreal · increment · continuity · tangent · slope · rate of change
Too small to consider
- minuteSixtieth of an hour
- microscopicToo small for eyes
- minusculeExtremely small in size
- vanishingCeasing to be visible
Things that cannot separate
- monadIndivisible fundamental unit
- ZenoGreek paradox thinker
- paradoxSeemingly absurd truth
- continuumUninterrupted, gradual sequence
divisibility · Aristotle · Berkeley · atomism · rigor · foundations
Smallest discrete unit
- perturbationState of being unsettled
- variationChange from a norm
- approximationNear but inexact value
- first-orderSimplest logical level
higher-order · Taylor expansion · linearization · small angle
derivative
Function's rate of change
- integralAntiderivative or crucial component
- LeibnizBaroque-era polymath philosopher-mathematician
- NewtonFamous scientific surname
differential · convergence · limit · hyperreal · increment · continuity · tangent · slope · rate of change · approximation
negligible
Too small to consider
- minuteSixtieth of an hour
- microscopicToo small for eyes
- minusculeExtremely small in size
vanishing · imperceptible · inappreciable · undetectable · evanescent
indivisibles
Things that cannot separate
continuum · divisibility · Aristotle · Berkeley · atomism · rigor · foundations
quantum
Smallest discrete unit
- perturbationState of being unsettled
- variationChange from a norm
- approximationNear but inexact value
first-order · higher-order · Taylor expansion · linearization · small angle
- calculusderivatives, integral, integrals, limits, differential calculus
- homeopathyremedies, calendula, dilutions, like cures like, hypericum
- hyperreals
- ArchimedesArchimedes screw, eureka, eureka moment, buoyancy, hydrostatics
- Greek mathematicsEuclid, Archimedes, Pythagoras, geometry, theorem
- Hypercomplex Mathquaternion, Clifford algebra, rotor, rotors, blade
infinitesimalsinfinities
Quantities without limit
infinity · the infinite · transfinite numbers · immensities · large numbers