Metamath Proof Explorer


Table of Contents - 20.3.6. Decimal expansion

Define a decimal expansion constructor. The decimal expansions built with this constructor are not meant to be used alone outside of this chapter. Rather, they are meant to be used exclusively as part of a decimal number with a decimal fraction, for example .

That decimal point operator is defined in the next section. The bulk of these constructions have originally been proposed by David A. Wheeler on 12-May-2015, and discussed with Mario Carneiro in this thread: https://groups.google.com/g/metamath/c/2AW7T3d2YiQ.

  1. cdp2
  2. df-dp2
  3. dp2eq1
  4. dp2eq2
  5. dp2eq1i
  6. dp2eq2i
  7. dp2eq12i
  8. dp20u
  9. dp20h
  10. dp2cl
  11. dp2clq
  12. rpdp2cl
  13. rpdp2cl2
  14. dp2lt10
  15. dp2lt
  16. dp2ltsuc
  17. dp2ltc
  18. Decimal point
    1. cdp
    2. df-dp
    3. dpval
    4. dpcl
    5. dpfrac1
    6. dpval2
    7. dpval3
    8. dpmul10
    9. decdiv10
    10. dpmul100
    11. dp3mul10
    12. dpmul1000
    13. dpval3rp
    14. dp0u
    15. dp0h
    16. rpdpcl
    17. dplt
    18. dplti
    19. dpgti
    20. dpltc
    21. dpexpp1
    22. 0dp2dp
    23. dpadd2
    24. dpadd
    25. dpadd3
    26. dpmul
    27. dpmul4
    28. threehalves
    29. 1mhdrd
  19. Division in the extended real number system
    1. cxdiv
    2. df-xdiv
    3. xdivval
    4. xrecex
    5. xmulcand
    6. xreceu
    7. xdivcld
    8. xdivcl
    9. xdivmul
    10. rexdiv
    11. xdivrec
    12. xdivid
    13. xdiv0
    14. xdiv0rp
    15. eliccioo
    16. elxrge02
    17. xdivpnfrp
    18. rpxdivcld
    19. xrpxdivcld