User:Lord Farin

About me
Just a mathematics graduate with a broad interest, trying to make mathematics more accessible.

For you, reader

 * Ever wondered how all those nice diagrams made it to your book? Check out the xymatrix package documentation.

Map of LF-Realm
My personal templates, sandboxes and the like:

User:Lord_Farin/Sandbox is my sandbox, which is used to test functionality, and prepare/attempt pages and structures. May have subpages attached.

User:Lord_Farin/SandboxTemplate is my sandbox template, in which I experiment with templates.

User:Lord Farin/Proof Structures is the place for proof templates I (and hopefully more people) tend to use.

User:Lord Farin/Tableau Proof Rules is where I keep templates for all allowed inferences in tableau proofs. This may appear as a bona fide page in the future.

User:Lord_Farin/Archive is a mixture between a graveyard and a safe haven for stuff which has nowhere else to go.

User:Lord_Farin/Backup documents old versions of pages I rebuilt from scratch.

Category:Lord_Farin's Stubs is the Category for pages I plan to finish later on.

User:Lord_Farin/Long-Term Projects is the place for things that are on even longer tracks than those in above Category; these are often meta-structural.

User:Lord_Farin/Books lists the books I have started to cover on PW.

Landmarks
I am particularly fond of the following contributions (all of which hence are my own work; i.e., I didn't copy the proof from some source):


 * Absolutely Convergent Generalized Sum Converges
 * Hilbert Space Direct Sum is Hilbert Space
 * Definition:Magma of Sets, an encapsulating notion from my hand

Postponed
I promised (to myself or others) to get back at these points but the moment I do is so far in the future I would forget if they weren't here:


 * Definition talk:Join
 * Equivalence of Boolean Lattice Definitions

Too lazy / Loose ends
These results are mostly trivial and I can't be bothered putting them up right now; please, feel free.


 * Generalize Zero and One are the only Consecutive Squares/Proof 2 to higher powers
 * Definition:Characteristic Function Operation (the operation $\chi_{(\cdot)}$ sending a subset to its char. fn)
 * Definition:Support Operation (the operation $\operatorname{supp}$ sending a function to its support)
 * Support Operation Inverse to Characteristic Function Operation
 * Inverse of Subset of Group is Inverse of Subset of Underlying Monoid (or some proper title)
 * Infimum of Upper Closure of Set

Natural Numbers

 * 1) Revisit:
 * 2) Natural Numbers are Comparable
 * 3) Natural Number Ordering is Transitive
 * 4) Natural Number Addition is Closed
 * 5) Properties of Natural Numbers
 * 6) Natural Numbers as Cardinals
 * 7) Product of Finite Sets is Finite
 * 8) Proper Subset of Finite Ordinal is Equivalent to Smaller Ordinal
 * 9) Equivalence of definitions of Natural Number Addition
 * 10) Definition for 1-based: Definition:Addition on 1-Based Natural Numbers
 * 11) Equivalence of definitions of ordering on $\N$

Follow-up projects

 * 1) Everything in Category:Natural Numbers needs a thorough review and possibly rewriting according to the new paradigm.
 * 2) Clear up Category:Natural Numbers/1-Based to a new, better category

Relation Theory

 * weaker/stronger or some other description of subsets of relations.
 * Definition:Difference of Relations
 * Difference of Relations is Relation

Category Theory

 * Projection Functor is Functor
 * Domain Functor is Functor
 * Codomain Functor is Functor
 * Morphism Category is Category
 * Composition Functor is Functor
 * Slice Functor is Functor
 * Coslice Category is Category
 * Singleton Poset is Terminal Object
 * Trivial Monoid is Initial Object, Trivial Monoid is Terminal Object
 * Contravariant Representable Functor is Functor
 * Category of Cones is Category
 * Category of Cocones is Category
 * Category of Groups is Category
 * Limit of Singleton
 * Functor to Product Category