Linked Open Sets

by Michael Brunnbauer

finally, hereditary sets have arrived in the Linked Open Data cloud!

You can use the following URIs to refer to some of them or retrieve machine readable data about them:

Natural numbers

https://www.brunni.de/sets/natural_number.cgi?number=number#set

Example: 10

Positive rational numbers

https://www.brunni.de/sets/rational_number.cgi?a=numerator&c=denominator#set

Example: 5/3

Arbitrary finite sets

https://www.brunni.de/sets/v6.cgi?number=index#set

Where index is a natural number. A set with index a is element of the set with index b iff bit a-1 of b-1 is 1.

See Von Neumann universe.

The natural number 0 (the empty set) has index 1.

The natural number 1 has index 2.

The natural number 2 has index 4.

The natural number 3 has index 12.

The natural number 4 has index 2060.

The natural number 5 has index 66185228434044942951864067458396061614989522267577311297802947435570493724401440549267868490798926773634494383968047143923956857140205406402740536087446083831052036848232439995904404992798007514718326043410570379830870463780085260619444417205199197123751210704970352727833755425876102776028267313405809429548880554782040765277562828362884238325465448520348307574943345990309941642666926723379729598185834735054732500415409883868361423159913770812218772711901772249553153402287759789517121744336755350465901655205184917370974202405586941211065395540765567663193297173367254230313612244182941999500402388195450053080385548.

The index of natural number 6 already has much more digits than the number of atoms in the know universe.

The last element of V₆ - which contains all 65536 elements of V₅ is here. The index of this set has 19729 decimal digits that are part of the URL - maybe your browser cannot handle this. This server should handle URLs with up to 32751 characters.

√2

https://www.brunni.de/sets/root_of_two.cgi#set