The On-Line Encyclopedia of Bongard Problems

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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.

BP386	BP394	BP904	BP922	BP926	BP931
BP956	BP997	BP1057	BP1072	BP1146	BP1148
BP1149	BP1150	BP1197	BP1199	BP1200	BP1201

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BP329

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	COMMENTS	`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`
	REFERENCE	`https://en.wikipedia.org/wiki/Countable_set`
	CROSSREFS	`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`
	KEYWORD	`math, meta (see left/right), links, keyword`
	WORLD	`bp_infinite_left_examples [smaller \| same \| bigger] zoom in right (left_uncountable_bp)`
	AUTHOR	`Leo Crabbe`

BP1024

One sorted left vs. one sorted right.

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	CROSSREFS	`Adjacent-numbered pages: BP1019 BP1020 BP1021 BP1022 BP1023 * BP1025 BP1026 BP1027 BP1028 BP1029`
	KEYWORD	`precise, allsorted, dual, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1025

Two consecutive numbers sorted left vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1020 BP1021 BP1022 BP1023 BP1024 * BP1026 BP1027 BP1028 BP1029 BP1030`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1026

Not an inequality solution vs. inequality solution.

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	CROSSREFS	`Adjacent-numbered pages: BP1021 BP1022 BP1023 BP1024 BP1025 * BP1027 BP1028 BP1029 BP1030 BP1031`
	KEYWORD	`precise, allsorted, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1028

An even number is the least sorted left vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1023 BP1024 BP1025 BP1026 BP1027 * BP1029 BP1030 BP1031 BP1032 BP1033`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1029

Multiple distinct differences between successive left numbers vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1024 BP1025 BP1026 BP1027 BP1028 * BP1030 BP1031 BP1032 BP1033 BP1034`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1031

"Less than ___ vs. greater than ___" vs. other solution.

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	CROSSREFS	`See the twin BP1039.` `Adjacent-numbered pages: BP1026 BP1027 BP1028 BP1029 BP1030 * BP1032 BP1033 BP1034 BP1035 BP1036`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1032

Left infinite vs. left finite.

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	CROSSREFS	`See BP1041 for right finite vs. right infinite. That is this Problem with with sides flipped and sides of mini-Problems flipped.` `See BP515 (left-finite) for a version that sorts links to Bongard Problems and not just about numbers, instead of images of Bongard Problems (miniproblems) about numbers.` `Adjacent-numbered pages: BP1027 BP1028 BP1029 BP1030 BP1031 * BP1033 BP1034 BP1035 BP1036 BP1037`
	KEYWORD	`precise, allsorted, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	CONCEPT	`finite_infinite (info \| search)`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1033

Left all even vs. some odd is left.

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	CROSSREFS	`Adjacent-numbered pages: BP1028 BP1029 BP1030 BP1031 BP1032 * BP1034 BP1035 BP1036 BP1037 BP1038`
	KEYWORD	`precise, allsorted, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1034

"Multiple of ___ vs. other number" vs. other solution.

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	CROSSREFS	`Adjacent-numbered pages: BP1029 BP1030 BP1031 BP1032 BP1033 * BP1035 BP1036 BP1037 BP1038 BP1039`
	KEYWORD	`precise, allsorted, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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