# sets (grouped)

A pattern of many things that are each different from the others but are bounded together by what is the same about them.

- Computed level: L3 (depth in the emergence graph, not abstraction)
- Status: review  ·  Domain: math  ·  Arena: abstract

## Emergence
**Emerges from:** [pattern](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-pattern.regularity), [others](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-others.distinct-entities), [boundary](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-boundary.limit), [difference](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-difference.relation)

**Through:** Pattern.regularity and difference.relation interact within space.extent and boundary.limit to separate others.distinct-entities into a collection defined by shared and excluded features.

**Novel properties:**
- distinct membership
- inclusive boundary
- abstract grouping

## Examples
- The periodic table organizes 118 elements into columns based on recurring chemical properties despite differing atomic structures. *(chemistry)*
- Linux distributions share the same kernel but vary in software packages, forming a family of distinct operating systems. *(computing)*
- The 27 EU member states retain individual governments but are bound by shared treaties and institutions. *(institutions)*

## Used by
- [autonomy](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-autonomy.self-governed) (L15)
- [bottleneck](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-bottleneck.constraint) (L8)
- [business](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-business.economic) (L8)
- [category](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-category.group) (L9)
- [chapter](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-chapter.section) (L18)
- [chokepoint](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-chokepoint.bottleneck) (L11)
- [class](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-class.category) (L5)
- [clothing](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-clothing.apparel) (L15)
- [collection](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-collection.group) (L5)
- [community](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-community.social) (L7)
- [context](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-context.surrounding-conditions) (L11)
- [control](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-control.ability) (L4)
- [data](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-data.information) (L7)
- [dependence](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-dependence.condition) (L11)
- [ecosystem](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-ecosystem.interdependent) (L15)
- [equipment](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-equipment.tool) (L9)
- [family](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-family.social) (L7)
- [first](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-first.order) (L4)
- [five](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-five.cardinal) (L6)
- [foundation](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-foundation.structural) (L11)
- [ground](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-ground.level) (L11)
- [history](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-history.record) (L7)
- [hundred](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-hundred.quantity) (L8)
- [impossibility](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-impossibility.unreachable) (L17)
- [including](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-including.general) (L4)
- [individual](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-individual.entity) (L5)
- [items](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-items.object) (L4)
- [jewelry](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-jewelry.accessory) (L14)
- [layer](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-layer.stratum) (L12)
- [line](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-line.geometric) (L12)
- [magazine](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-magazine.publication) (L17)
- [national](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-national.political) (L9)
- [noun](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-noun.language) (L10)
- [options](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-options.choice) (L8)
- [people](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-people.social) (L6)
- [poker](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-poker.game) (L17)
- [policy](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-policy.governance) (L8)
- [process](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-process.general) (L4)
- [related](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-related.association) (L4)
- [series](https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-series.ordered) (L10)

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*Canonical: https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-sets.grouped*  
*Structured data: https://emergencemachine.com/tools/lexicon/what-is-the-meaning-of-sets.grouped.json*  
*Every definition provably resolves to space, time, energy and pattern.*