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Showing 31–60 of 1709 reference entries

Physics · MeasurementCaesium-133 defining frequency

ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Its numerical value is fixed exactly in SI units.

DefinitionMathematics & logic · InformationClassical propositions and connectives

Classical logic combines truth-valued propositions using defined connectives.

DefinitionMathematics & logicAxioms, deduction and mathematical proof

A mathematical proof derives a conclusion within stated assumptions and rules.

MethodMathematics & logic · InformationSets, membership and basic operations

A set specifies membership without counting duplicate listings.

DefinitionMathematics & logic · InformationFunctions, domain and codomain

A function assigns exactly one output to each input in its domain.

DefinitionMathematics & logic · InformationMathematical induction

A base case and general successor step establish a predicate on all nonnegative integers.

MethodMathematics & logic · MeasurementEuclidean right triangles and the Pythagorean theorem

In a Euclidean right triangle, squared leg lengths sum to the squared hypotenuse length.

Mathematical statementMathematics & logic · PhysicsSine, cosine and the unit circle

Sine and cosine are unit-circle coordinates whose squared values sum to one.

Mathematical statementMathematics & logic · InformationComplex numbers

A complex number has real coordinates a and b and an imaginary unit satisfying i²=−1.

DefinitionMathematics & logic · Information · PhysicsLinear maps and matrix representation

A linear map preserves linear combinations and has a matrix once bases are chosen.

DefinitionMathematics & logicLimit of a real function

A finite limit controls output error through sufficiently small input distance.

DefinitionMathematics & logic · PhysicsDerivative at a point

A derivative is a finite limit of local difference quotients.

DefinitionMathematics & logic · PhysicsDefinite integral and signed accumulation

A definite integral is the limiting signed accumulation of small contributions.

DefinitionMathematics & logic · PhysicsFundamental theorem of calculus

Continuity connects differentiation with integration.

Mathematical statementMathematics & logic · InformationProbability space and axioms

A probability assigns nonnegative, normalised, countably additive weights to events.

DefinitionMathematics & logic · InformationConditional probability and independence

Conditioning restricts attention to an event of positive probability.

DefinitionMathematics & logic · InformationExpected value of a discrete random variable

Expected value weights possible values by their probabilities.

DefinitionMathematics & logic · MeasurementConfidence interval for a population mean

A confidence level describes repeated-sampling coverage of an interval procedure.

MethodInformation · Mathematics & logicBits and unsigned binary encoding

A bit has two possible states; a fixed-width unsigned binary word encodes an integer.

DefinitionInformation · Mathematics & logicShannon entropy of a discrete distribution

Shannon entropy measures uncertainty in a specified probability distribution.

DefinitionInformationAlgorithm and decision procedure

An algorithm specifies effective steps; a decision procedure must terminate on every permitted input.

MethodInformation · Mathematics & logicUndecidability of the halting problem

No total algorithm decides halting for every program and input in a general computation model.

Mathematical statementInformation · Mathematics & logicAsymptotic upper bounds and big O

Big O bounds eventual growth up to a fixed constant factor.

DefinitionMeasurementSI base units

Seven named base units organize the SI quantity system.

DefinitionMeasurementSI decimal prefixes

Prefix symbols specify decimal scale factors.

DefinitionMeasurementMetrological traceability

Connect a result to a reference through documented calibrations.

DefinitionMeasurement · Mathematics & logicFirst-order uncertainty propagation

Combine input uncertainty through a measurement model.

MethodMeasurement · Physics · Mathematics & logicDimensional consistency

Use dimensions to detect impossible quantity equations.

MethodPhysics · Earth & cosmosNewtonian gravitation

An inverse-square force models attraction between point masses.

ModelPhysicsFrequency, wavelength and phase speed

Relate a periodic wave's spatial and temporal repetition.

Definition
MethodSource checked

Dimensional consistency

MeasurementPhysicsMathematics & logic

Use dimensions to detect impossible quantity equations.

Key knowledge

In a physically meaningful quantity equation, added terms and the two sides must have compatible dimensions. Dimensional agreement is necessary but cannot determine a missing dimensionless numerical factor.

Conditions and scope

  • Distinguish a quantity equation from a numerical equation tied to specified units.
  • Dimensional consistency alone does not prove a physical model.
Sources · 4

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. University Physics Volume 1 · Dimensional AnalysisOpenStaxTextbook chapteropenstax.orgRead source
  2. International Vocabulary of Metrology (VIM3)Joint Committee for Guides in Metrology (JCGM)Reference guideInternational Vocabulary of Metrology, 3rd edition: 1.22International Vocabulary of Metrology, 3rd edition: 1.25jcgm.bipm.org
  3. Units and Measurement · Physics (2026–27 reprint)National Council of Educational Research and Training (NCERT)Textbook chapter · PDFncert.nic.inRead source

Evidence and review

OpenStax 1.4, dimensional-consistency rules and limitation for dimensionless factors.

2026-10-10 · Consistency test and its limitation only; no general physical law is inferred from dimensions.

Foundational review

2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.

Sources from other places

Agreement within this scope

Dimensional homogeneity checks necessary compatibility but cannot determine dimensionless factors or prove a model correct.

A dimensionally consistent expression can still be physically wrong.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–1 of 1 relationships

Scientific relationships · 1 / 1

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Uses definition
    Relationship sources · 3

    Linked statements

    • A quantity kind groups mutually comparable quantities. A quantity dimension expresses dependence on base quantities as a product of powers; quantities of the same kind have the same dimension, but equal dimensions need not imply the same kind. Energy and torque both have dimension ML²T⁻² yet have different meanings. Dimension-one quantities can also represent different kinds, so an omitted unit does not remove physical meaning.

    This relation concerns the stated quantity kind and physical dimension claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

Entry detailsPermanent link to this entry ↗
Record identity
measurement-dimensional-analysis
Revision
core.1
Structured reference record
Essential core · first collection