From 207eecae121f7a4257721a55117f805edd9e8eda Mon Sep 17 00:00:00 2001
From: julian laplace <julescarbon@gmail.com>
Date: Tue, 12 Aug 2025 15:39:30 +0200
Subject: commentary

---
 index.html | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/index.html b/index.html
index d4fa42c..c27174b 100644
--- a/index.html
+++ b/index.html
@@ -694,10 +694,10 @@
           numerator and denominator that are both whole numbers. Notes in equal
           temperament, however, are separated by a semitone of 1 to the 12th
           root of 2 (1:<super>12</super>√2), an irrational number, and can only
-          be approximated by rationals. By definition, any real number might be
-          at the theoretical limit of the Lambdoma in any direction, but by
-          definition these numbers are not rational numbers, and are thus only
-          approximated by the intervals of the Lambdoma.
+          be approximated by rationals. While all rational numbers are real
+          numbers, not all real numbers are rational, and true equal-tempered
+          invervals are only <i>approximated</i> by the intervals of the
+          Lambdoma.
         </p>
 
         <p>
@@ -712,7 +712,7 @@
           to the natural numbers. Though there are infinitely many rational
           numbers, by their nature they are discrete, countable, and not
           completely dense. Between any two rational numbers, there lies an
-          uncountable continuity of real numbers in ℝ.
+          uncountable continuity of irrational real numbers in ℝ.
         </p>
 
         <h2>thank you!</h2>
@@ -735,7 +735,7 @@
           support!
         </p>
 
-        <p>Jules LaPlace / <a href="/">asdf.us</a> / 2018-2025</p>
+        <p>Jules LaPlace / <a href="/">asdf.us</a> / 2017-2025</p>
       </div>
       <br />
     </div>
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