The On-Line Encyclopedia of Bongard Problems

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The completed version of the collection indicated by the objects is finite vs. the completed version of the collection indicated by the objects is infinite.

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	COMMENTS	`Related to BP870 and BP792.` `An example with clusters of perfect numbers of dots would be sorted ambiguously, for the time being. Unfortunately the 3rd smallest perfect number is 496. - Leo Crabbe, Oct 18 2024`
	CROSSREFS	`Adjacent-numbered pages: BP375 BP376 BP377 BP378 BP379 * BP381 BP382 BP383 BP384 BP385`
	KEYWORD	`math, creativeexamples, traditional, rules, miniworlds, collection`
	CONCEPT	`finite_infinite (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP543

Image depicting infinitely many objects vs. image depicting finitely many objects.

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	COMMENTS	`Another solution is "evokes infinity vs. not so." Or "seen as having arbitrarily fine detail." All left examples show objects getting smaller and smaller and closer and closer together approaching some limit within the box.`
	CROSSREFS	`Adjacent-numbered pages: BP538 BP539 BP540 BP541 BP542 * BP544 BP545 BP546 BP547 BP548`
	KEYWORD	`nice, abstract, concept, infinitedetail`
	CONCEPT	`finite_infinite (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP792

Complete finite collection versus incomplete infinite collection.

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	COMMENTS	`Related to BP379 and BP380.` `EX10061 can ambiguously be taken to be self-referential as the set of left-hand examples (which would make the right hand solution only "incomplete sets") or the class of finite sets.`
	CROSSREFS	`Adjacent-numbered pages: BP787 BP788 BP789 BP790 BP791 * BP793 BP794 BP795 BP796 BP797`
	KEYWORD	`abstract, creativeexamples, rules, miniworlds, collection`
	CONCEPT	`completeness (info \| search),` `finite_infinite (info \| search)`
	WORLD	`collection_of_objects_same_type [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP915

Finite number of dots vs. infinite number of dots.

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	CROSSREFS	`Adjacent-numbered pages: BP910 BP911 BP912 BP913 BP914 * BP916 BP917 BP918 BP919 BP920`
	KEYWORD	`less, notso, spectrum, number, example, left-null, impossible, experimental`
	CONCEPT	`finite_infinite (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

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`

BP1059

No infinite nesting vs. some infinite nesting.

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	CROSSREFS	`Adjacent-numbered pages: BP1054 BP1055 BP1056 BP1057 BP1058 * BP1060 BP1061 BP1062 BP1063 BP1064`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`finite_infinite (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1067

There is an infinite one-one-one-one-... chain present vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1062 BP1063 BP1064 BP1065 BP1066 * BP1068 BP1069 BP1070 BP1071 BP1072`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`finite_infinite (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1069

Infinitely many branches vs. finitely many branches.

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	CROSSREFS	`Adjacent-numbered pages: BP1064 BP1065 BP1066 BP1067 BP1068 * BP1070 BP1071 BP1072 BP1073 BP1074`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`finite_infinite (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1070

Dead end vs. no dead ends.

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	CROSSREFS	`Adjacent-numbered pages: BP1065 BP1066 BP1067 BP1068 BP1069 * BP1071 BP1072 BP1073 BP1074 BP1075`
	KEYWORD	`perfect, infinitedetail`
	CONCEPT	`finite_infinite (info \| search),` `fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1079

A left example can be verified to fit left by checking only finitely many layers deep vs. not so.

BP1058^↔	BP1060^↔	BP1061^↔	BP1062^↔	BP1063^↔	BP1065^↔
BP1068^↔	BP1077^↔	BP1058	BP1059	BP1061	BP1066
BP1070

BP1059^↔	BP1066^↔	BP1067^↔	BP1069^↔	BP1070^↔	BP1071^↔
BP1060	BP1062	BP1063	BP1065	BP1067	BP1068
BP1069	BP1071	BP1077

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	CROSSREFS	`Adjacent-numbered pages: BP1074 BP1075 BP1076 BP1077 BP1078 * BP1080 BP1081 BP1082 BP1083 BP1084`
	KEYWORD	`meta (see left/right), links, side, wellfounded`
	CONCEPT	`semidecidable (info \| search),` `finite_infinite (info \| search)`
	WORLD	`recursive_boxes_bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

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