Integral vs. Integer — What's the Difference?

Essential component.

Whole number.

Mathematical operation.

Number line.

Completeness.

Counting example.

System functionality.

Algebraic foundation.

Inherent part.

Basic arithmetic.

In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

An integer (from the Latin integer meaning "whole") is colloquially defined as a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+1/2, and √2 are not.

Of or denoted by an integer.

A member of the set of positive whole numbers {1, 2, 3, ... }, negative whole numbers {-1, -2, -3, ... }, and zero {0}.

Necessary to make a whole complete; essential or fundamental

A number which is not a fraction; a whole number

A function of which a given function is the derivative, i.e. which yields that function when differentiated, and which may express the area under the curve of a graph of the function.

A thing complete in itself.

Essential or necessary for completeness; constituent

A complete unit or entity.

Possessing everything essential; entire.

(arithmetic) A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.

Expressed or expressible as or in terms of integers.

A complete entity; a whole number, in contradistinction to a fraction or a mixed number.

Expressed as or involving integrals.

Any of the natural numbers (positive or negative) or zero

A complete unit; a whole.

A number computed by a limiting process in which the domain of a function, often an interval or planar region, is divided into arbitrarily small units, the value of the function at a point in each unit is multiplied by the linear or areal measurement of that unit, and all such products are summed.

A definite integral.

An indefinite integral.

Constituting a whole together with other parts or factors; not omittable or removable

(mathematics) Of, pertaining to, or being an integer.

(mathematics) Relating to integration.

(obsolete) Whole; undamaged.

(mathematics) One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a long s: ∫, or a variant thereof.

(specifically) Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.

(mathematics) A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diverge. In notation, the domain of integration is indicated either below the sign, or, if it is an interval, with its endpoints as sub- and super-scripts, and the function being integrated forming part of the integrand (or, generally, differential form) appearing in front of the integral sign.

(mathematics) An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;

The fluent of a given fluxion in Newtonian calculus.

Lacking nothing of completeness; complete; perfect; uninjured; whole; entire.

Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.

Of, pertaining to, or being, a whole number or undivided quantity; not fractional.

A whole; an entire thing; a whole number; an individual.

An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent.

The result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)

Existing as an essential constituent or characteristic;

Constituting the undiminished entirety; lacking nothing essential especially not damaged;

Integral refers to something that is essential or fundamentally necessary to make a whole complete.

An integer is a whole number that can be positive, negative, or zero, not including fractions or decimals.

Integers are used in counting objects, measuring temperatures below zero, and calculating debts, among other applications.

"Honest communication is integral to maintaining strong personal relationships."

An integer's positivity or negativity is determined by its value relative to zero: positive if above zero, negative if below.

Integers serve as the foundation for arithmetic operations, number theory, and are integral in defining more complex number systems.

Something is considered integral if its absence would compromise the whole's completeness or functionality.

Negative numbers are represented as integers with a minus sign, indicating their position on the negative side of the number line.

No, while integral has a specific meaning in calculus, it also broadly applies to essential components or aspects in various fields.

Integers include whole numbers without fractional or decimal parts, distinguishing them from real or rational numbers that can include fractions.

Yes, certain components or features can be described as integral to a technology's functionality or design.

Yes, the integration process in calculus embodies the integral concept, calculating quantities that contribute to a whole.

In calculus, integrals calculate the area under a curve, representing accumulation or continuous addition of quantities.

Yes, integers can be used in statistical data, representing counts, losses, gains, or other discrete variables.

No, only whole numbers are integers; numbers with fractional or decimal components are not.