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Cantor–Bernstein–Schroeder theorem

theorem that, if there exist injective functions in both directions between two sets, then there exists a bijection between them
Intangible theorem Q1033910
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Cantor–Bernstein–Schroeder theorem

Summary

Cantor–Bernstein–Schroeder theorem is a theorem[1]. It ranks in the top 10% of theorem entities by monthly Wikipedia readership (285 views/month).[2]

Key Facts

  • Cantor–Bernstein–Schroeder theorem's image is recorded as CantorEquivalenceTheorem1887b.gif[3].
  • Cantor–Bernstein–Schroeder theorem's instance of is recorded as theorem[4].
  • Felix Bernstein is named after Cantor–Bernstein–Schroeder theorem[5].
  • Ernst Schröder is named after Cantor–Bernstein–Schroeder theorem[6].
  • Georg Cantor is named after Cantor–Bernstein–Schroeder theorem[7].
  • Cantor–Bernstein–Schroeder theorem's Commons category is recorded as Schröder-Bernstein theorem[8].
  • Cantor–Bernstein–Schroeder theorem's Freebase ID is recorded as /m/015x7k[9].
  • Cantor–Bernstein–Schroeder theorem's proved by is recorded as Richard Dedekind[10].
  • Cantor–Bernstein–Schroeder theorem's proved by is recorded as Felix Bernstein[11].
  • Cantor–Bernstein–Schroeder theorem's different from is recorded as Cantor's theorem[12].
  • Cantor–Bernstein–Schroeder theorem's uses is recorded as principle of excluded middle[13].
  • Cantor–Bernstein–Schroeder theorem's statement describes is recorded as injection[14].
  • Cantor–Bernstein–Schroeder theorem's studied by is recorded as set theory[15].
  • Cantor–Bernstein–Schroeder theorem's MathWorld ID is recorded as Schroeder-BernsteinTheorem[16].
  • Cantor–Bernstein–Schroeder theorem's nLab ID is recorded as Cantor-Schroeder-Bernstein theorem[17].
  • Cantor–Bernstein–Schroeder theorem's schematic is recorded as Cantor-bernstein.svg[18].
  • Cantor–Bernstein–Schroeder theorem's schematic is recorded as Cantor-Bernstein.png[19].
  • Cantor–Bernstein–Schroeder theorem's schematic is recorded as Cantor1.png[20].
  • Cantor–Bernstein–Schroeder theorem's schematic is recorded as Cantor-Bernstein orig.png[21].
  • Cantor–Bernstein–Schroeder theorem's maintained by WikiProject is recorded as WikiProject Mathematics[22].
  • Cantor–Bernstein–Schroeder theorem's Microsoft Academic ID is recorded as 88151527[23].
  • Cantor–Bernstein–Schroeder theorem's ProofWiki ID is recorded as Cantor-Bernstein-Schröder_Theorem[24].
  • Cantor–Bernstein–Schroeder theorem's Namuwiki ID is recorded as 슈뢰더-베른슈타인 정리[25].
  • Cantor–Bernstein–Schroeder theorem's Treccani's Enciclopedia della Matematica ID is recorded as teorema-di-cantor-schroder-bernstein[26].
  • Cantor–Bernstein–Schroeder theorem's logical consequence of is recorded as Zermelo–Fraenkel set theory[27].

Why It Matters

Cantor–Bernstein–Schroeder theorem ranks in the top 10% of theorem entities by monthly Wikipedia readership (285 views/month).[2] It has Wikipedia articles in 17 language editions, a strong signal of global cultural recognition.[28] It is known by 51 alternative names across languages and contexts.[29]

Related Entities

Ernst Schröder Georg Cantor Richard Dedekind

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.
  6. [8] ↑ . wikidata.org.
  7. [9] ↑ . Freebase Data Dumps. wikidata.org.
  8. [10] ↑ . wikidata.org.
  9. [11] ↑ . wikidata.org.
  10. [12] ↑ . wikidata.org.
  11. [13] ↑ . wikidata.org.
  12. [14] ↑ . wikidata.org.
  13. [15] ↑ . wikidata.org.
  14. [16] ↑ . wikidata.org.
  15. [17] ↑ . wikidata.org.
  16. [18] ↑ . wikidata.org.
  17. [19] ↑ . wikidata.org.
  18. [20] ↑ . wikidata.org.
  19. [21] ↑ . wikidata.org.
  20. [22] ↑ . wikidata.org.
  21. [23] ↑ . wikidata.org.
  22. [24] ↑ . wikidata.org.
  23. [25] ↑ . wikidata.org.
  24. [26] ↑ . wikidata.org.
  25. [27] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [28] ↑ . Wikidata sitelinks. wikidata.org.
  3. [29] ↑ . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Cantor–Bernstein–Schroeder theorem. Retrieved May 3, 2026, from https://4ort.xyz/entity/cantor-bernstein-schroeder-theorem
MLA “Cantor–Bernstein–Schroeder theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/cantor-bernstein-schroeder-theorem.
BibTeX @misc{4ortxyz_cantor-bernstein-schroeder-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Cantor–Bernstein–Schroeder theorem}}, year = {2026}, url = {https://4ort.xyz/entity/cantor-bernstein-schroeder-theorem}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Cantor–Bernstein–Schroeder theorem — https://4ort.xyz/entity/cantor-bernstein-schroeder-theorem (retrieved 2026-05-03)

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