Mark Dominus @mjd@mathstodon.xyz

YOU MATHEMATICIANS THINK YOU SO SMART, THAN EXPLAIN THIS!!1!

Heck, there are some quite interesting subsets of \(\Bbb N\) that are closed under multiplication. Consider for example { 54, 64, 81, 96, 144, 216, 256, 324, 384, 486, 576, 729, 864, 1024, 196, 1536, 1944, 2304, 2916, 3456, 4096, 4374, 5184, 6144, 6561, 7776, 9216, 11664, 13824, 16384, 17496, 20736, 24576, 26244, 31104, 36864, 39366, 46656, 55296, 59049, 65536, 69984, 82944, 98304, … }.
That's the set of all integers that are (a) \( 2^i3^j \), (b) \( 5k\pm1\), and (c) at least \(54\).

Consider the family F that contains the subsets of \(\Bbb Q\) that are closed under multiplication. Some elements of F are well-known (\( \varnothing\), \( \Bbb Q \) itself; others less so. (Consider the set of rational numbers with denominators of the form \( 5k \pm 1\)] or the set with denominators \( 2^i3^j\) .)

\( F \setminus\{\varnothing\} \) has a very interesting lattice structure.

Today I learned that there is such a thing as a “quinternion”! https://shitpost.plover.com/t/til/20191222.html

Color-blind readers: I would appreciate your feedback on the diagrams in https://blog.plover.com/math/gcm.html . Please reply here or by email to mjd@pobox.com . Thanks.

New math post on my blog: The least common divisor and the greatest common multiple https://blog.plover.com/math/gcm.html

New math post on my blog: More fair cake-cutting https://blog.plover.com/math/cake-2.html

New math post on my blog: Incenters of chocolate-iced cakes https://blog.plover.com/math/cake.html

New math post on my blog: Breaking pills https://blog.plover.com/math/breaking-pills.html

I decided that the world needed to see the Maclaurin series thrashing like a screen door in a hurricane.

New math post on my blog: Convergence of Taylor series https://blog.plover.com/math/exponential-2.html

Wikipedia has this animation of the Maclaurin series converging for e^x, but it emphasizes the right-hand side, where the behavior is much less bizarre, and only hints at the left-hand side where the partial sums flap back and forth like a screen door in a hurricane.

New math post on my blog: The exponential function is a miracle https://blog.plover.com/math/exponential.html

New math post on my blog: Technical devices for reducing the number of axioms https://blog.plover.com/math/technical-devices.html

New math post on my blog: Obtuse axiomatization of category theory https://blog.plover.com/math/freyd-theory.html

New math post on my blog: Projection morphisms are (not) epic https://blog.plover.com/math/epic-projections.html

New math post on my blog: The inside-outness of category theory https://blog.plover.com/math/category-theory-outlook.html

It's late. I misread a notification as “favourited your cactus”.

New math post on my blog: What's the difference between 0/0 and 1/0? https://blog.plover.com/math/division-by-zero.html