cartesian product
noun
Simple meaning
The set of all possible ordered pairs of elements, the being first from X, the second from Y, written X×Y.
Pronunciation
Say it like this:
kahrteezhuhnprahduhktSay the bold part a little louder.
IPA pronunciation (US)
kɑɹˈtiʒənpɹɑdəkt
This word is pronounced essentially the same in American and British English, so one transcription covers both.
IPA (International Phonetic Alphabet) is a standard way of writing speech sounds.
Definition
Everyday modern meanings first, grouped by part of speech.
noun
set theoryof two sets X and Y
The set of all possible ordered pairs of elements, the being first from X, the second from Y, written X×Y. Formally, the set (x,y);|;x∈X;and;y∈Y.
(geometry, of an m-dimensional space X and an n-dimensional space Y) An (m+n)-dimensional space, formally composed of all possible ordered pairs of points from X and Y, but thought of as an independent (m+n)-dimensional space (in the sense that if, e.g. X and Y are vector spaces, the elements of X×Y are thought of as (m+n)-tuples instead of ordered pairs) and written X×Y.
databases
All possible combinations of rows between all of the tables listed.
Word Aura™
How this word commonly comes across.
Aura for this meaning
This meaning: (set theory, of two sets X and Y) The set of all possible ordered pairs of elements, the being first from X, the second from Y, written X×Y. Formally, the set (x,y);|;x∈X;and;y∈Y.
Used this way, cartesian product is a specialist word that usually carries little praise or criticism of its own. This is a mathematical use: it is defined precisely and belongs to working with figures and calculations rather than to ordinary conversation.
- Emotional tone
- Neutral
- Formality
- Specialist/technical
- Intensity
- Not strongly marked
- How common
- Specialized
- Connotation
- Clinical and technical
- Usage feel
- Technical and specialized
Where it naturally appears
- Mathematics
- Geometry
- Academic writing
- Education/classroom
Usage note
In general conversation this sense usually needs explaining — outside its field, people reach for a plainer word.
Word Aura describes common impressions, not a measurement. Tone changes with sentence, speaker, relationship and situation.
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Dictionary data from Wiktionary via the Free Dictionary API. Simple meanings, combinations and word intelligence are built from verified reference data, no AI is used to load this page.