Welcome To Math Notes

Welcome to my math notebook. Here you will find my perspective on logic. It's not too dissimilar to propositional calculus, but I don't bother with sufficiency of connectives and I don't have a problem with infinite input variables.

Generalized Truth Functions

Logic is all about choices. An idea is true or false, a student is present or absent, a switch is on or off. All the truth tables and specialized language of propositional calculus is geared to exploring these choices and their consequences.

Truth Function Algebra

Algebra is all about keeping a predicate true while rearranging the variables that define its shape. Identities introduce new or repeats of existing variables, commutativity switches the location of variables, and associativity changes what functions variables are in.

Miscellaneous Theorems

A mind without choice is only truth, and only uncertain. As life presents choice, and we fain understanding, that uncertainty gives way to belief in what is possible, and what is not...