i) A class X is ๐ก๐๐๐๐ ๐๐ก๐๐ฃ๐ if every member of a member of X is a member of X.
Note: this implies "members of members of members" of X are also members of X, and so on all the way down.
ii) A set is an ๐๐๐๐๐๐๐ if it is transitive and well-ordered by โ.
@mirandaisrisen i've never watched it, but i suspect it's a fairly loose and highly sensationalized connection between the show and actual mathematical forensics.
i) A class X is ๐ก๐๐๐๐ ๐๐ก๐๐ฃ๐ if every member of a member of X is a member of X.
Note: this implies "members of members of members" of X are also members of X, and so on all the way down.
ii) A set is an ๐๐๐๐๐๐๐ if it is transitive and well-ordered by โ.
@SpottlessMarxx this is not based on "conditioning", it's my conclusion based on a lifetime of studying math, science, and programming. no the terrain is not the map - the universe has an existence independent of our mental machinations.
i don't believe "mathematics is the language of the universe". the universe does what it does, it doesn't need a "language". math is a human attempt to describe the universe, and as such, it is an abstraction, an approximation, and at least one step removed from reality.
not only is mathematics a fascinating field of study on its own, its intersection with science is broad, its history is rich, and it even serves on social media as a test tube for the DunningโKruger effect.
@Colwiz yes, i am aware that both Gรถdel and Einstein embraced what i would summarize as "Platonic realism", however it's worth noting that this is out of step with the views of most of their coworkers, which i call "formalist idealism".
@DiracDeltaFunk not really, considering much of math was invented by scientists for that purpose. it's like saying its crazy that geometry is so good for designing buildings.
@ChristianJF27 no i think you're engaging in sophistry. if no conscious beings existed, who would be doing the imagining and the mental operation of dividing?
@w4xyy some structures are embodied in reality, but humans have to add the abstraction themselves. there's no inherent similarity between 3 trees and 3 stars, other than the human made abstraction of number. however much of math (such as advanced set theory) has no parallel in reality.
@JoelTHpostHack there are large domains of mathematics which have nothing to do with science or the empirical universe (such as advanced set theory) - they only chart out areas of our minds.