Metamath Proof Explorer


Table of Contents - 20.39.7.152. Limits for sequences of extended real numbers

Textbooks generally use a single symbol to denote the limit of a sequence of real numbers. But then, three distinct definitions are usually given: one for the case of convergence to a real number, one for the case of limit to and one for the case of limit to . It turns out that these three definitions can be expressed as the limit w.r.t. to the standard topology on the extended reals. In this section, a relation is defined that captures all three definitions (and can be applied to sequences of extended reals, also), see dfxlim2.

  1. clsxlim
  2. df-xlim
  3. xlimrel
  4. xlimres
  5. xlimcl
  6. rexlimddv2
  7. xlimclim
  8. xlimconst
  9. climxlim
  10. xlimbr
  11. fuzxrpmcn
  12. cnrefiisplem
  13. cnrefiisp
  14. xlimxrre
  15. xlimmnfvlem1
  16. xlimmnfvlem2
  17. xlimmnfv
  18. xlimconst2
  19. xlimpnfvlem1
  20. xlimpnfvlem2
  21. xlimpnfv
  22. xlimclim2lem
  23. xlimclim2
  24. xlimmnf
  25. xlimpnf
  26. xlimmnfmpt
  27. xlimpnfmpt
  28. climxlim2lem
  29. climxlim2
  30. dfxlim2v
  31. dfxlim2
  32. climresd
  33. climresdm
  34. dmclimxlim
  35. xlimmnflimsup2
  36. xlimuni
  37. xlimclimdm
  38. xlimfun
  39. xlimmnflimsup
  40. xlimdm
  41. xlimpnfxnegmnf2
  42. xlimresdm
  43. xlimpnfliminf
  44. xlimpnfliminf2
  45. xlimliminflimsup
  46. xlimlimsupleliminf