index f7ed3ab..332bbc9 100644
@@ -16,7 +16,7 @@ a set is a collection of things. that's it. but from this absurdly simple starti
**complement** (Aᶜ): everything not in A. the opposite. "people who don't like pizza."
-these four operations let you manipulate categories with precision. every database query (SQL's WHERE, JOIN, UNION, EXCEPT) is set operations on rows — a fact that makes [[stem/computer-science|computer science]] fundamentally dependent on set-theoretic thinking. every search engine query (AND, OR, NOT) is set operations on documents.
+these four operations let you manipulate categories with precision. every database query (SQL's WHERE, JOIN, UNION, EXCEPT) is set operations on rows — a fact that makes [[computer-science|computer science]] fundamentally dependent on set-theoretic thinking. every search engine query (AND, OR, NOT) is set operations on documents.
## MECE: mutually exclusive, collectively exhaustive
@@ -43,7 +43,7 @@ the discipline of asking "is this MECE?" catches a huge number of analytical err
venn diagrams are the visual language of set theory. two or three overlapping circles can clarify relationships that paragraphs of text obscure.
-but venn diagrams have limits. with 4+ sets, they become unwieldy. and they encourage you to think about small, discrete categories when sometimes the right framework is continuous (a spectrum, not a partition). knowing when to use set-theoretic thinking and when to use continuous thinking (more like [calculus](/wiki/structural/calculus-as-thinking) or [linear algebra](/wiki/structural/linear-algebra-as-thinking)) is itself a useful skill.
+but venn diagrams have limits. with 4+ sets, they become unwieldy. and they encourage you to think about small, discrete categories when sometimes the right framework is continuous (a spectrum, not a partition). knowing when to use set-theoretic thinking and when to use continuous thinking (more like [[calculus-as-thinking|calculus]] or [[linear-algebra-as-thinking|linear algebra]]) is itself a useful skill.
## binary classification as set membership
@@ -51,7 +51,7 @@ the most basic question in set theory: "is x in the set S?" yes or no.
this is exactly the binary classification problem in machine learning: is this email spam or not? is this transaction fraudulent or not? is this patient sick or not? the entire field of classification is about drawing boundaries in some feature space that define the set of "positive" examples.
-connections to [probability](/wiki/immediate/probability-in-daily-life): in practice, you rarely get a hard yes/no. you get a probability — "this email is 87% likely to be spam." the boundary between "in the set" and "out of the set" becomes fuzzy. fuzzy set theory formalizes this.
+connections to [[probability-in-daily-life|probability]]: in practice, you rarely get a hard yes/no. you get a probability — "this email is 87% likely to be spam." the boundary between "in the set" and "out of the set" becomes fuzzy. fuzzy set theory formalizes this.
## set operations on ideas
@@ -77,6 +77,6 @@ this is why definitions matter. not pedantically, but fundamentally. sloppy defi
## the deep point
-set theory is the mathematics of classification. the impulse to classify connects to [[immediate/ordering-and-comparison|ordering and comparison]] — you can't sort things into sets without first deciding what makes them similar or different. taken further, the study of how sets relate to each other through notions of "nearness" and continuity leads to [[structural/topology-as-thinking|topology]], which generalizes set theory into the study of shape and space.
+set theory is the mathematics of classification. the impulse to classify connects to [[ordering-and-comparison|ordering and comparison]] — you can't sort things into sets without first deciding what makes them similar or different. taken further, the study of how sets relate to each other through notions of "nearness" and continuity leads to [[topology-as-thinking|topology]], which generalizes set theory into the study of shape and space.
-in a world drowning in information, the ability to categorize precisely — to define boundaries, check for completeness, identify overlaps, and reason about relationships between categories — is one of the most practical mathematical skills there is. this kind of precise categorical reasoning is itself a form of [[structural/abstraction-as-power|abstraction]]: stripping away particulars to focus on structure. you don't need to know the axiom of choice to benefit from thinking in sets.
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+in a world drowning in information, the ability to categorize precisely — to define boundaries, check for completeness, identify overlaps, and reason about relationships between categories — is one of the most practical mathematical skills there is. this kind of precise categorical reasoning is itself a form of [[abstraction-as-power|abstraction]]: stripping away particulars to focus on structure. you don't need to know the axiom of choice to benefit from thinking in sets.
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