1 files changed, 7 insertions, 7 deletions
diff --git a/mathematics/logic.md b/mathematics/logic.md
index e19cb52..0760a8c 100644
--- a/mathematics/logic.md
+++ b/mathematics/logic.md
@@ -18,9 +18,9 @@ and many others.
 
 ## orders of logic
 
-### [propositional logic](https://ncatlab.org/nlab/show/propositional+logic)
+### propositional logic
 
-**propositional logic** or **zeroth-order logic** deals with raw *propositions*.
+[**propositional logic**](https://ncatlab.org/nlab/show/propositional+logic) or **zeroth-order logic** deals with raw *propositions*.
 **propositions** are statements that *reduce* to a **truth value**.
 truth values are classically either true or false. in non-classical logics, this can differ.
 
@@ -28,11 +28,11 @@ the basic foundations of propositional logic are as follows:
 
 notation | definition
 ---------|--------------
+0        | *false*
+1        | *true*
 p        | a *proposition*
 ¬p       | *not* p
 p → q   | *if* p *then* q, p *implies* q
-0        | *false*
-1        | *true*
 
 several logical connectives are *derivable* from the above:
 
@@ -40,17 +40,17 @@ notation | derivation | definition
 ------|---------------------|----
 p ∨ q | ¬p → q             | p *or* q, *disjunction*
 p ∧ q | ¬(p → ¬q)          | p *and* q, *conjunction*
-p → q | ¬p ∨ q             | p *implies* q, (material) *implication* (again)
+p → q | ¬p ∨ q             | p *implies* q, (material) *implication*
 p ↔ q | (p → q) ∧ (q → p) | p *if and only if* q, p *iff* q
 p ⊕ q | (p ∨ q) ∧ ¬(p ∧ q) | p *exclusively or* q, p *xor* q
 p ↑ q | ¬(p ∧ q)           | p *not both* q, p *nand* q
 p ↓ q | ¬(p ∨ q)           | *neither* p *nor* q, p *nor* q
 
 note that several of these definitions are circular.
-our choice in $¬$ and $→$ as the primitive connectives is thus arbitrary.
+our choice in ¬ and → as the primitive connectives is thus arbitrary.
 interestingly, ↑ and ↓ are *functionally complete*: we may define all other connectives in terms of them.
 
-<details>
+<details markdown="block">
 <summary>aside: nand and nor</summary>
 
 notation | definition