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Charles Wells. Professor Emeritus of Math at Case Western Reserve University. Websites:

http://www.abstractmath.org/Word%20Press/ http://www.abstractmath.org/ http://www.cwru.edu/artsci/math/wells/home.html


Jul
7
comment What technical and/or theoretical challenges are involved in automatically extracting proofs from books and papers into Coq code?
The problems in understanding mathematical English, even in formally written papers, is well described in the book The Language of mathe­matics, by Mohan Ganesalingam, and many other examples are given in my website athttp://www.abstractmath.org/MM/MMLangMath.htm
Jun
16
awarded  Yearling
Sep
24
awarded  Autobiographer
Feb
8
accepted If $a$ is irrational, must $a^a$ be irrational?
Feb
6
asked If $a$ is irrational, must $a^a$ be irrational?
Oct
26
awarded  Good Answer
Nov
11
awarded  Nice Answer
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14
awarded  Yearling
Jan
24
awarded  Nice Answer
Oct
15
awarded  Yearling
Apr
28
awarded  Good Answer
Nov
28
awarded  Nice Answer
Oct
15
awarded  Yearling
Aug
15
comment Graphical representation of mathematical structures (in the spirit of unified modeling language)
A specific technique in category theory for building structures is outlined in Graph Based Logic and Sketches, by Atish Bagchi and Charles Wells, arxiv.org/abs/0809.3023. This was specifically designed to be translated easily into an object-oriented program.
Aug
14
comment Is there a notion of congruence relation for essentially algebraic structures?
Some colimits blow up even with algebraic theories. For example, the underlying set of the coproduct of two groups in the category of groups is not the coproduct (disjoint sum) of the underlying sets.
Aug
13
comment Collapsing objects in a category
My answer to Peter Arndt's question contains some information about this question.
Aug
13
comment Is there a notion of congruence relation for essentially algebraic structures?
Congruences on categories work very nicely when restricted to bijections on objects. This has attracted a lot of interest. Extension Theories for Categories, by Charles Wells. cwru.edu/artsci/math/wells/pub/pdf/catext.pdf For the following references I thank Peter Webb: An Introduction to the Representations and Cohomology of Categories, by Peter Webb. math.umn.edu/~webb/Publications/CategoryAlgebras.pdf G. Hoff, Cohomologies et extensions de categories, Math. Scand. 74 (1994), 191--207. H.-J. Baues and G. Wirsching, Cohomology of small categories, JPAA 38
Aug
13
revised Is there a notion of congruence relation for essentially algebraic structures?
Added info about effective equivalence relations.
Aug
13
answered Is there a notion of congruence relation for essentially algebraic structures?
Jul
31
comment Question on the decimal expansion of algebraic numbers
If you can give a precise statement of "not too many small periodic blocks in a row" that would apparently be a counterexample to Borel's conjecture. But Borel's conjecture may have a more precise statement that rules this out.