Instructors who would like to create their own Lurch course materials using the rule libraries and content from my Math 299 course can find supporting materials here. NOTE: some of this is under construction.
Cumulative Topics – each link one opens a blank Lurch document whose context consists of the rules for that topic, and those from the topics above it.
and
, or
, not
, implies
, iff
, and contradiction
(view rules)forall
$\left(\forall\right)$, exists
$\left(\exists\right)$, equality
$\left(=\right)$, unique existence
$\left(\exists!\right)$ (view rules)less than
$\left(\lt\right)$, divides
$\left(\mid\right)$, prime
, even
, odd
(view rules)summation
$\left(\sum\right)$, Fibonnaci numbers
$\left(F_n\right)$, factorial
$\left(!\right)$, multinomial coefficients
$\binom{n}{k}$, binomial coefficients
, exponentiation
$\left(z^n\right)$ (view rules)in
$\left(\in\right)$, subset
$\left(\subseteq\right)$, intersection
$\left(\cap\right)$, union
$\left(\cup\right)$, complement
$\left(‘\right)$, set difference
$\left(\setminus\right)$, powerset
$\left(\mathscr{P}\right)$, Cartesian product
$\left(\times\right)$, finite set
$\left(\{ \ldots \}\right)$, tuple
$\langle\ldots\rangle$, Indexed Union
$\left(\bigcup\right)$, Indexed Intersection
$\left(\bigcap\right)$, Set Builder notation
$\left(\{ z : \ldots\}\right)$ (view rules)maps
$\left(f\colon A \to B\right)$, function application
$\left(f(x)\right)$, maps to
$\left(\mapsto\right)$, image
$\left(f(U)\right)$, identity map
$\left(\text{id}_A\right)$ inverse image
$\left(f^\text{inv}(U)\right)$, composition
$\left(\circ\right)$, inverse function
$\left(f^{-1}\right)$, injective
, surjective
, bijective
(view rules)reflexive
, symmetric
, transitive
, irreflexive
, antisymmetric
, total
, partial order
, strict partial order
, total order
, equivalence relation
, partition
, equivalence class
$[a]$ (view rules)Some Other Useful Contexts
Prove it! Topics – each link one opens a blank Lurch document whose context consists of the rules for that topic.
or
, not
, and contradiction
(view rules)