Count to 1000, social experiment

PUBLIQclopAccountant
Non-Fungible Trixie -
Magical Inkwell - Wrote MLP fanfiction consisting of at least around 1.5k words, and has a verified link to the platform of their choice

Pubilq Phirm
55,702

Bumping my offer for variant counting threads to the top of the new page. I’ll treat it as a no if no one expresses interest by the time this page is finished.
Would anyone be interested in either of the following counting threads? I’d make the OP to provide some examples, as the rules are best described by example.
  1. Counting in cyclicly decreasing1 bases
  2. Count ALL the rational numbers!
1 Cyclicly-increasing bases also work, but decreasing allows for a better OP example to show the pattern.
Bryon

55,703
While it’s a cool idea PUBLIQ, at the same time, it would be kinda confusing, even if you would explain the rules.
PUBLIQclopAccountant
Non-Fungible Trixie -
Magical Inkwell - Wrote MLP fanfiction consisting of at least around 1.5k words, and has a verified link to the platform of their choice

Pubilq Phirm
55,706

I’ll give examples for each. Each bullet point is a separate post.

Count ALL the rational numbers!

  1. 1/1, 2/1, 1/2, 1/3, 2/2, 3/1, 1/4, 2/3
  2. 3/2
  3. 4/1, 5/1, 4/2, 3/3, 2/4, 1/5, 1/6, 2/5
  4. 3/4
  5. 4/3
  6. 5/2
  7. 6/1, 7/1, 6/2, 5/3
It’s a zigzag path through the rational numbers (that’s how you prove they have the same cardinality as the natural numbers we’re counting in this thread).
Each poster continues until they hit a non-reducible fraction that does not have 1 as either the numerator or denominator. Once a fraction with a 1 is reached, the other part of the fraction is incremented by 1 and then the pattern starts to head toward putting the 1 in the other slot while keeping the same sum of numerator and denominator.

Cyclic base counting

  1. 116
  2. 215
  3. 314
  4. 413
  5. 512
  6. 611
  7. 710
  8. 89
  9. 118
  10. 137
  11. 156
  12. 225
  13. 314
  14. 1123
  15. 11112
  16. 1016
  17. 1215
Cycling bases in the other direction wouldn’t show how this differs from plain counting until post 16.
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