Infinitesimal vs. Infinity — What's the Difference?
By Fiza Rafique & Maham Liaqat — Updated on May 6, 2024
Infinitesimal refers to something extremely small, approaching zero; infinity describes something without any bounds or limits.
Difference Between Infinitesimal and Infinity
Table of Contents
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Key Differences
Infinitesimal describes quantities so small that they cannot be measured using standard means, often used in mathematics to represent quantities approaching zero. Infinity, on the other hand, represents an unbounded quantity that is conceptually larger than any number.
In calculus, infinitesimal is used to explain concepts like derivatives and integrals by considering the limits of functions as they approach zero. Whereas infinity is used to discuss limits that grow without bound or describe the size of uncountably large sets.
In physics, the concept of infinitesimal is crucial for explaining continuous changes and movements in a mathematical model. On the other hand, infinity often appears in theoretical physics when discussing concepts like spacetime in the context of the universe's extent.
In everyday language, infinitesimal is sometimes used figuratively to mean something extremely small or insignificant. Infinity, conversely, is used to express something endless or immeasurable, like the concept of forever.
Philosophically, infinitesimal challenges our understanding of the very small and how it interacts with the finite, suggesting a bridge between the quantifiable and the theoretical. Infinity challenges our comprehension of the very large, questioning the limits of human understanding and the cosmos.
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Comparison Chart
Concept
Approaches zero, almost negligible
No limits, endlessly large
Use in Calculus
Basis for derivatives and integrals
Used in limits, series
Significance
Essential in detailed analysis
Symbolic of boundlessness
Philosophical
Challenges finite understanding
Explores the concept of endlessness
Everyday Use
Means very small
Means endless or boundless
Compare with Definitions
Infinitesimal
Mathematically significant yet practically intangible.
Infinitesimal quantities are fundamental in the study of calculus.
Infinity
Used to describe time or space without end.
The road stretched to infinity under the vast sky.
Infinitesimal
Extremely small or minute.
The chances of winning the lottery are infinitesimal.
Infinity
Unbounded or limitless.
His patience seemed to have infinity.
Infinitesimal
Approaching zero.
In calculus, an infinitesimal change is one that is smaller than any measurable amount.
Infinity
Greater than any assignable quantity or countable number.
There are infinity possibilities in this scenario.
Infinitesimal
Nearly non-existent.
The infinitesimal error did not affect the experiment's outcome.
Infinity
A concept in mathematics and physics describing something without any bound.
The mathematical series approaches infinity.
Infinitesimal
Immeasurably small.
He made an infinitesimal adjustment to the machine's settings.
Infinity
Endlessly large, unlimited.
The universe stretches into infinity.
Infinitesimal
In mathematics, an infinitesimal or infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinity-th" item in a sequence.
Infinity
Infinity is that which is boundless or endless, or something that is larger than any real or natural number. It is often denoted by the infinity symbol shown here.
Infinitesimal
Immeasurably or incalculably minute.
Infinity
The state or quality of being infinite
The infinity of space
Infinitesimal
(Mathematics) Capable of having values approaching zero as a limit.
Infinity
A number greater than any assignable quantity or countable number (symbol ∞)
The transmission approaches 100% as the frequency tends to infinity
Infinitesimal
An immeasurably or incalculably minute amount or quantity.
Infinity
The quality or condition of being infinite.
Infinitesimal
(Mathematics) A function or variable continuously approaching zero as a limit.
Infinity
Unbounded space, time, or quantity.
Infinitesimal
Incalculably, exceedingly, or immeasurably minute; vanishingly small.
Do you ever get the feeling that you are but an infinitesimal speck, swallowed by the vastness of the universe and beyond?
Infinity
An indefinitely large number or amount.
Infinitesimal
(mathematics) Of or pertaining to values that approach zero as a limit.
Infinity
(Mathematics) The limit that a function is said to approach at x = a when (x) is larger than any preassigned number for all x sufficiently near a.
Infinitesimal
(informal) Very small.
Infinity
A range in relation to an optical system, such as a camera lens, representing distances great enough that light rays reflected from objects within the range may be regarded as parallel.
Infinitesimal
(mathematics) A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).
Infinity
A distance setting, as on a camera, beyond which the entire field is in focus.
Infinitesimal
Infinitely or indefinitely small; less than any assignable quantity or value; very small.
Infinity
(uncountable) endlessness, unlimitedness, absence of a beginning, end or limits to size.
Infinitesimal
An infinitely small quantity; that which is less than any assignable quantity.
Infinity
A number that has an infinite numerical value that cannot be counted.
Infinitesimal
Infinitely or immeasurably small;
Two minute whiplike threads of protoplasm
Reduced to a microscopic scale
Infinity
An idealised point which is said to be approached by sequences of values whose magnitudes increase without bound.
Infinity
(uncountable) A number which is very large compared to some characteristic number. For example, in optics, an object which is much further away than the focal length of a lens is said to be "at infinity", as the distance of the image from the lens varies very little as the distance increases further.
Infinity
The symbol ∞. Category:en:Infinity
Infinity
Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity.
There can not be more infinities than one; for one of them would limit the other.
Infinity
Unlimited capacity, energy, excellence, or knowledge; as, the infinity of God and his perfections.
Infinity
Endless or indefinite number; great multitude; as an infinity of beauties.
Infinity
A quantity greater than any assignable quantity of the same kind.
Infinity
That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.
Infinity
Time without end
Common Curiosities
How is infinity used in calculus?
Infinity in calculus is used to describe limits that increase without bounds and for discussing infinite series and their convergence.
Can something be infinitesimally large?
No, infinitesimal specifically refers to quantities that are extremely small, not large.
Is infinity a number?
Infinity is not a number but a concept representing something without any limit or end.
What does infinitesimal mean in mathematics?
In mathematics, infinitesimal refers to a quantity that is closer to zero than any standard real number, yet not zero itself.
What role does infinitesimal play in theoretical physics?
Infinitesimal quantities are key in theoretical physics for defining precise models of continuous phenomena.
How does the concept of infinity impact philosophy?
In philosophy, infinity prompts discussions about the nature of the universe, existence, and the limits of human comprehension.
Can we visualize infinitesimal quantities?
Infinitesimal quantities, by nature, are too small to visualize directly and are instead understood through mathematical concepts.
What are practical examples of infinitesimal quantities?
In physics, infinitesimal quantities can describe minute changes in velocity or position over extremely short time intervals.
What is the difference between infinitesimal and microscopic?
Infinitesimal refers to quantities much smaller than can be seen or measured, even when compared to microscopic sizes, which are merely very small but still measurable.
How do different cultures perceive the concept of infinity?
Different cultures and philosophical traditions may interpret infinity in various metaphysical, spiritual, or practical contexts.
Is infinity always related to size or quantity?
While often related to size or quantity, infinity can also relate to concepts like time (endless duration) or space (endless expanse).
What is an example of infinity in nature?
Concepts like the endless expansion of the universe or an unbounded horizon can illustrate infinity in nature.
Does modern technology use the concept of infinitesimal?
Yes, concepts involving infinitesimals are used in engineering and computer science, particularly in algorithms that approximate continuous processes.
Do infinity and infinitesimal appear in everyday speech?
Yes, both terms are used in everyday speech, often figuratively to describe very large or very small amounts.
What philosophical questions does infinity raise?
Infinity raises philosophical questions about the nature of the universe, the possibility of an actual infinite, and the limitations of human understanding.
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Written by
Fiza RafiqueFiza Rafique is a skilled content writer at AskDifference.com, where she meticulously refines and enhances written pieces. Drawing from her vast editorial expertise, Fiza ensures clarity, accuracy, and precision in every article. Passionate about language, she continually seeks to elevate the quality of content for readers worldwide.
Co-written by
Maham Liaqat
