Metamath Proof Explorer


Table of Contents - 2.6.14. Cardinal number arithmetic

For cardinal arithmetic, we follow [Mendelson] p. 258. Rather than defining operations restricted to cardinal numbers, we use disjoint union df-dju () for cardinal addition, Cartesian product df-xp () for cardinal multiplication, and set exponentiation df-map () for cardinal exponentiation. Equinumerosity and dominance serve the roles of equality and ordering. If we wanted to, we could easily convert our theorems to actual cardinal number operations via carden, carddom, and cardsdom. The advantage of Mendelson's approach is that we can directly use many equinumerosity theorems that we already have available.

  1. undjudom
  2. endjudisj
  3. djuen
  4. djuenun
  5. dju1en
  6. dju1dif
  7. dju1p1e2
  8. dju1p1e2ALT
  9. dju0en
  10. xp2dju
  11. djucomen
  12. djuassen
  13. xpdjuen
  14. mapdjuen
  15. pwdjuen
  16. djudom1
  17. djudom2
  18. djudoml
  19. djuxpdom
  20. djufi
  21. cdainflem
  22. djuinf
  23. infdju1
  24. pwdju1
  25. pwdjuidm
  26. djulepw
  27. onadju
  28. cardadju
  29. djunum
  30. unnum
  31. nnadju
  32. nnadjuALT
  33. ficardadju
  34. ficardun
  35. ficardunOLD
  36. ficardun2
  37. ficardun2OLD
  38. pwsdompw
  39. unctb
  40. infdjuabs
  41. infunabs
  42. infdju
  43. infdif
  44. infdif2
  45. infxpdom
  46. infxpabs
  47. infunsdom1
  48. infunsdom
  49. infxp
  50. pwdjudom
  51. infpss
  52. infmap2