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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
DefinitionSource checked

SI decimal prefixes

Measurement

Prefix symbols specify decimal scale factors.

Key knowledge

SI prefixes multiply a unit by an exact power of ten: kilo (k) gives 10³, milli (m) gives 10⁻³ and micro (μ) gives 10⁻⁶. The complete adopted range extends from quecto (q, 10⁻³⁰) to quetta (Q, 10³⁰).

Conditions and scope

  • Prefixes are decimal; they do not define binary information prefixes.
  • Apply an exponent to the whole prefixed unit: (mm)² means (10⁻³ m)².
Sources · 4

References

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

  1. Bureau International des Poids et Mesures (BIPM)2 sources
    1. The International System of Units, ninth edition, version 4.01 (2026)Bureau International des Poids et Mesures (BIPM)Reference guidebipm.orgRead source
    2. The International System of Units, 9th edition, version 4.01 (2026)Bureau International des Poids et Mesures (BIPM)Reference guidebipm.orgRead source
  2. Metric (SI) PrefixesNational Institute of Standards and Technology (NIST)Reference guidenist.govRead source
  3. O Sistema Internacional de Unidades (SI) · 2ª edição luso-brasileiraInmetro and Instituto Português da QualidadeReference guide · PDFgov.brRead source

Evidence and review

SI Brochure chapter 3, Table 7 and 2022 prefix resolution; NIST current table.

2026-10-10 · Named prefix factors, case and exponent rule only; the entire prefix table is available at the source.

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

SI prefixes are decimal factors from 10−30 to 10^30; powers apply to the complete prefixed unit.

Decimal prefixes do not become binary factors in computing.

Related reference entries

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

Showing 1–3 of 3 relationships

Scientific relationships · 3 / 3

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

  1. Related to
    Relationship sources · 2

    Decimal prefix factors supply exact scale conversions for compatible SI units.

  2. Related to
    Relationship sources · 1

    Linked statements

    • Write SI unit symbols upright and with their prescribed case; symbols have no plural endings or abbreviation periods. Separate the numerical value from its unit with a space, including °C. Plane-angle °, ′ and ″ are exceptions to that space. Attach a prefix directly to its unit symbol. Use a space or centred dot for multiplied units, and parentheses or negative exponents to make divisions unambiguous.

    An attached prefix forms part of the unit symbol; it is not a separate factor in reader typography.

  3. Uses definition
    Relationship sources · 2

    Linked statements

    • The kilogram is the SI base unit of mass and already contains the historical prefix kilo. Decimal multiples and submultiples of mass are named by attaching one prefix to gram, not by stacking a new prefix on kilogram: 1 mg=10⁻⁶ kg and 1 μg=10⁻⁹ kg.

    Uses the exact decimal factors milli and micro while explaining the special attachment convention.

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Record identity
measurement-si-prefixes
Revision
core.1
Structured reference record
Essential core · first collection