It's very useful to practice thinking about elementary set theory *without* thinking directly about elements. Spend some time thinking about sets *only* in terms of functions. Any function `f : A -> B` cuts an "A-shaped picture" out of B. In the special case where A is a

It's kind of wild that truth tables are such a recent idea. People have been studying logic for literally thousands of years, but truth tables were introduced in the early 1900s!

Terence Tao has released a new #LeanLang project that connects #FormalVerification with #MathematicsEducation: The companion to "Analysis I" is intended to provide a new avenue for engaging with the proofs and exercises in Tao's foundational "Analysis I" text. 👇

Space and logic are closely related! Imagine you're observing some physical object, like a coffee cup. But each observation you can make is only a *finite* observation. That is, an observation you can make in a finite amount of time. For instance, "it's too hot" (maybe that's

Apple is defrosting 😔

The Next 700 Substitution Notations

syntax is kiki, semantics is bouba

'There may, indeed, be other applications of the system [i.e. lambda calculus] than its use as a logic.' -- Alonzo Church, 1932

there's pre-syntax but what about post-semantics 🤔