Search: keyword:math
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| BP560 |
| There exists a closed trail that hits each edge exactly once vs. not so. |
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| BP562 |
| There exists a closed trail that hits each vertex exactly once vs. not so. |
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| BP563 |
| Bongard Problems such that there is a way of making an infinite list of all relevant possible left-sorted examples vs. Bongard Problems where there is no such way of listing all left-sorted examples. |
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COMMENTS
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Left-sorted Problems have the keyword "left-listable" on the OEBP.
All the possible left examples for the BPs on the left side of this problem could be listed in one infinite sequence. Right examples here are Problems for which no such sequence can exist.
This depends on deciding what images should be considered "the same thing", which is subjective and context-dependent.
All examples in this Bongard Problem have an infinite left side (they do not have the keyword left-finite).
The mathematical term for a set that can be organized into an infinite list is a "countably infinite" set, as opposed to an "uncountably infinite" set.
Another related idea is a "recursively enumerable" a.k.a. "semi-decidable" set, which is a set that a computer program could list the members of.
The keyword "left-listable" is meant to be for the more general idea of a countable set, which does not have to do with computer algorithms.
Note that this is not just BP940 (right-listable) flipped.
It seems in practice, Bongard Problems that are left-listable are usually also right-listable because the whole class of relevant examples is listable. A keyword for just plain "listable" may be more useful. Or instead keywords for left- versus right- semidecidability, in the sense of computing. - Aaron David Fairbanks, Jan 10 2023 |
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REFERENCE
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https://en.wikipedia.org/wiki/Countable_set |
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CROSSREFS
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See left-finite, which distinguishes between a finite left side and infinite left side.
"Left-listable" BPs are typically precise.
Adjacent-numbered pages:
BP558 BP559 BP560 BP561 BP562 * BP564 BP565 BP566 BP567 BP568
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KEYWORD
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math, meta (see left/right), links, keyword
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WORLD
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bp_infinite_left_examples [smaller | same | bigger]
zoom in right (left_uncountable_bp)
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AUTHOR
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Leo Crabbe
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| BP569 |
| Triangular number of dots vs. non-triangular number of dots |
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COMMENTS
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All examples in this Problem are groups of black dots.
The nth triangular number is the sum over the natural numbers from 1 to n, where n > 0. Note: 0 is the 0th triangular number. The first few triangular numbers are 0, 1, 3 (= 1+2) and 6 (= 1+2+3) |
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CROSSREFS
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Adjacent-numbered pages:
BP564 BP565 BP566 BP567 BP568 * BP570 BP571 BP572 BP573 BP574
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KEYWORD
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nice, precise, allsorted, notso, number, math, left-narrow, left-null, help, preciseworld
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WORLD
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dots [smaller | same | bigger]
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AUTHOR
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Leo Crabbe
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| BP576 |
| Vertices may be partitioned into two sets such that no two vertices in the same set are connected versus not so. |
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| BP788 |
| Graph contains a "loop" a.k.a. cycle (cyclic) versus graph is acyclic. |
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| BP790 |
| The leftmost two add (as vectors) to the right versus no two add to a third. |
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| BP791 |
| The leftmost two angles measured from thin line add to the rightmost versus no two angles add to a third. |
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