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dense-set · Nov 13, 2024 · b1a4c09 · b1a4c09
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diff --git a/.DS_Store b/.DS_Store
diff --git a/_quarto.yml b/_quarto.yml
@@ -5,6 +5,7 @@ project:
   resources:
     - files/
     - non-math/
+    - blog/
     - notes/
     - now/
     - records/
@@ -30,8 +31,8 @@ website:
         href: blog/index.qmd
       - text: Non-math
         href: non-math/index.qmd
-      - text: Now
-        href: now/index.qmd
+      #- text: Now
+      #  href: now/index.qmd
 
     right: 
       - text: "{{< iconify clarity email-solid >}}"

diff --git a/blog/steele-csmc/ch-1.qmd b/blog/steele-csmc/ch-1.qmd
@@ -79,7 +79,7 @@ The following stronger result also oozes out of the above proof:
   \end{equation*}
 :::
 
-Note that @prp-additiveIneq can also be derived from @prp-CSinR since $\sqrt{x}\sqrt y\le (x^2 + y^2)/2$ for $x, y\ge 0$. Conversely, we may derive @prp-CSinR (even for the infinite case) from @prp-additiveIneq as well by *normalizing*. Just make the following replacements: $a_j\to a_j\big/\sum_i a_i^2$ and $b_j\to b_j\big/\sum_i b_i^2$.
+Note that @prp-additiveIneq can also be derived from @prp-CSinR since $\sqrt{x}\sqrt y\le (x^2 + y^2)/2$ for $x, y\ge 0$. Conversely, we may derive @prp-CSinR (even for the infinite case) from @prp-additiveIneq as well by *normalizing*. Just make the following replacements: $a_j\to a_j\big/\sqrt{\sum_i a_i^2}$ and $b_j\to b_j\big/\sqrt{\sum_i b_i^2}$.
 
 ::: column-margin
   *"Normalization gives us a systematic way to pass from an additive to a multiplicative inequality."*

diff --git a/docs/blog/index.html b/docs/blog/index.html
@@ -2,14 +2,14 @@
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>
 
 <meta charset="utf-8">
-<meta name="generator" content="quarto-1.4.551">
+<meta name="generator" content="quarto-1.5.57">
 
 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
 <meta name="author" content="Sarthak">
 <meta name="description" content="Personal website for Sarthak">
 
-<title>Blog | dense set</title>
+<title>Blog | dense set – {{&lt; var website.title &gt;}}</title>
 <style>
 code{white-space: pre-wrap;}
 span.smallcaps{font-variant: small-caps;}
@@ -97,7 +97,7 @@
 </script>
 <style>html{ scroll-behavior: smooth; }</style>
 
-  <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
+  <script src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6"></script>
   <script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml-full.js" type="text/javascript"></script>
 
 <script type="text/javascript">
@@ -141,7 +141,7 @@
     <span class="navbar-title">dense set</span>
     </a>
   </div>
-          <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarCollapse" aria-controls="navbarCollapse" aria-expanded="false" aria-label="Toggle navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
+          <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarCollapse" aria-controls="navbarCollapse" role="menu" aria-expanded="false" aria-label="Toggle navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
   <span class="navbar-toggler-icon"></span>
 </button>
           <div class="collapse navbar-collapse" id="navbarCollapse">
@@ -162,10 +162,6 @@
     <a class="nav-link" href="../non-math/index.html"> 
 <span class="menu-text">Non-math</span></a>
   </li>  
-  <li class="nav-item">
-    <a class="nav-link" href="../now/index.html"> 
-<span class="menu-text">Now</span></a>
-  </li>  
 </ul>
             <ul class="navbar-nav navbar-nav-scroll ms-auto">
   <li class="nav-item">
@@ -190,7 +186,7 @@
   </li>  
 </ul>
           </div> <!-- /navcollapse -->
-          <div class="quarto-navbar-tools">
+            <div class="quarto-navbar-tools">
   <a href="" class="quarto-color-scheme-toggle quarto-navigation-tool  px-1" onclick="window.quartoToggleColorScheme(); return false;" title="Toggle dark mode"><i class="bi"></i></a>
 </div>
       </div> <!-- /container-fluid -->
@@ -230,7 +226,7 @@ <h1 class="title">Blog</h1>
 
 <div class="quarto-listing quarto-listing-container-default" id="listing-listing">
 <div class="list quarto-listing-default">
-<div class="quarto-post image-right" data-index="0" data-listing-date-sort="1680287400000" data-listing-file-modified-sort="1712065334782" data-listing-date-modified-sort="NaN" data-listing-reading-time-sort="15" data-listing-word-count-sort="2856">
+<div class="quarto-post image-right" data-index="0" data-listing-date-sort="1680287400000" data-listing-file-modified-sort="1712837587684" data-listing-date-modified-sort="NaN" data-listing-reading-time-sort="15" data-listing-word-count-sort="2856">
 <div class="thumbnail">
 <p><a href="../blog/steele-csmc/ch-1.html" class="no-external"></a></p><a href="../blog/steele-csmc/ch-1.html" class="no-external">
 <div class="listing-item-img-placeholder card-img-top" >&nbsp;</div>
@@ -439,18 +435,7 @@ <h3 class="no-anchor listing-title">
     }
     return false;
   }
-  const clipboard = new window.ClipboardJS('.code-copy-button', {
-    text: function(trigger) {
-      const codeEl = trigger.previousElementSibling.cloneNode(true);
-      for (const childEl of codeEl.children) {
-        if (isCodeAnnotation(childEl)) {
-          childEl.remove();
-        }
-      }
-      return codeEl.innerText;
-    }
-  });
-  clipboard.on('success', function(e) {
+  const onCopySuccess = function(e) {
     // button target
     const button = e.trigger;
     // don't keep focus
@@ -482,15 +467,37 @@ <h3 class="no-anchor listing-title">
     }, 1000);
     // clear code selection
     e.clearSelection();
+  }
+  const getTextToCopy = function(trigger) {
+      const codeEl = trigger.previousElementSibling.cloneNode(true);
+      for (const childEl of codeEl.children) {
+        if (isCodeAnnotation(childEl)) {
+          childEl.remove();
+        }
+      }
+      return codeEl.innerText;
+  }
+  const clipboard = new window.ClipboardJS('.code-copy-button:not([data-in-quarto-modal])', {
+    text: getTextToCopy
   });
+  clipboard.on('success', onCopySuccess);
+  if (window.document.getElementById('quarto-embedded-source-code-modal')) {
+    // For code content inside modals, clipBoardJS needs to be initialized with a container option
+    // TODO: Check when it could be a function (https://github.com/zenorocha/clipboard.js/issues/860)
+    const clipboardModal = new window.ClipboardJS('.code-copy-button[data-in-quarto-modal]', {
+      text: getTextToCopy,
+      container: window.document.getElementById('quarto-embedded-source-code-modal')
+    });
+    clipboardModal.on('success', onCopySuccess);
+  }
     var localhostRegex = new RegExp(/^(?:http|https):\/\/localhost\:?[0-9]*\//);
     var mailtoRegex = new RegExp(/^mailto:/);
       var filterRegex = new RegExp("?var:website\.site-url");
     var isInternal = (href) => {
         return filterRegex.test(href) || localhostRegex.test(href) || mailtoRegex.test(href);
     }
     // Inspect non-navigation links and adorn them if external
- 	var links = window.document.querySelectorAll('a[href]:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external):not([aria-hidden]):not(.dropdown-item):not(.quarto-navigation-tool)');
+ 	var links = window.document.querySelectorAll('a[href]:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external):not([aria-hidden]):not(.dropdown-item):not(.quarto-navigation-tool):not(.about-link)');
     for (var i=0; i<links.length; i++) {
       const link = links[i];
       if (!isInternal(link.href)) {

diff --git a/docs/blog/index.qmd b/docs/blog/index.qmd
@@ -0,0 +1,11 @@
+---
+title: "Blog"
+listing:
+  contents: steele-csmc
+  sort: "date desc"
+  type: default
+  # categories: true
+  # sort-ui: true
+  # filter-ui: true
+title-block-banner: true
+---
diff --git a/docs/blog/steele-csmc/_metadata.yml b/docs/blog/steele-csmc/_metadata.yml
@@ -0,0 +1,8 @@
+# options specified here will apply to all posts in this folder
+
+# freeze computational output
+# (see https://quarto.org/docs/projects/code-execution.html#freeze)
+freeze: true
+
+# Enable banner style title blocks
+title-block-banner: true
diff --git a/docs/blog/steele-csmc/ch-1.html b/docs/blog/steele-csmc/ch-1.html
@@ -2,15 +2,15 @@
 <html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>
 
 <meta charset="utf-8">
-<meta name="generator" content="quarto-1.4.551">
+<meta name="generator" content="quarto-1.5.57">
 
 <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
 
 <meta name="author" content="Sarthak">
 <meta name="dcterms.date" content="2023-04-01">
 <meta name="description" content="Personal website for Sarthak">
 
-<title>Starting with Cauchy | dense set</title>
+<title>Starting with Cauchy | dense set – {{&lt; var website.title &gt;}}</title>
 <style>
 code{white-space: pre-wrap;}
 span.smallcaps{font-variant: small-caps;}
@@ -67,7 +67,7 @@
 </script>
 <style>html{ scroll-behavior: smooth; }</style>
 
-  <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
+  <script src="https://cdnjs.cloudflare.com/polyfill/v3/polyfill.min.js?features=es6"></script>
   <script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml-full.js" type="text/javascript"></script>
 
 <script type="text/javascript">
@@ -111,7 +111,7 @@
     <span class="navbar-title">dense set</span>
     </a>
   </div>
-          <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarCollapse" aria-controls="navbarCollapse" aria-expanded="false" aria-label="Toggle navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
+          <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarCollapse" aria-controls="navbarCollapse" role="menu" aria-expanded="false" aria-label="Toggle navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
   <span class="navbar-toggler-icon"></span>
 </button>
           <div class="collapse navbar-collapse" id="navbarCollapse">
@@ -132,10 +132,6 @@
     <a class="nav-link" href="../../non-math/index.html"> 
 <span class="menu-text">Non-math</span></a>
   </li>  
-  <li class="nav-item">
-    <a class="nav-link" href="../../now/index.html"> 
-<span class="menu-text">Now</span></a>
-  </li>  
 </ul>
             <ul class="navbar-nav navbar-nav-scroll ms-auto">
   <li class="nav-item">
@@ -160,7 +156,7 @@
   </li>  
 </ul>
           </div> <!-- /navcollapse -->
-          <div class="quarto-navbar-tools">
+            <div class="quarto-navbar-tools">
   <a href="" class="quarto-color-scheme-toggle quarto-navigation-tool  px-1" onclick="window.quartoToggleColorScheme(); return false;" title="Toggle dark mode"><i class="bi"></i></a>
 </div>
       </div> <!-- /container-fluid -->
@@ -266,7 +262,7 @@ <h2 class="anchored" data-anchor-id="notes">Notes</h2>
     \sum_i a_i b_i\le \frac{1}{2}\sum_i a_i^2 + \frac{1}{2}\sum_i b_i^2.
   \end{equation*}\]</span></p>
 </div>
-<p>Note that <a href="#prp-additiveIneq" class="quarto-xref">Proposition&nbsp;2</a> can also be derived from <a href="#prp-CSinR" class="quarto-xref">Proposition&nbsp;1</a> since <span class="math inline">\(\sqrt{x}\sqrt y\le (x^2 + y^2)/2\)</span> for <span class="math inline">\(x, y\ge 0\)</span>. Conversely, we may derive <a href="#prp-CSinR" class="quarto-xref">Proposition&nbsp;1</a> (even for the infinite case) from <a href="#prp-additiveIneq" class="quarto-xref">Proposition&nbsp;2</a> as well by <em>normalizing</em>. Just make the following replacements: <span class="math inline">\(a_j\to a_j\big/\sum_i a_i^2\)</span> and <span class="math inline">\(b_j\to b_j\big/\sum_i b_i^2\)</span>.</p>
+<p>Note that <a href="#prp-additiveIneq" class="quarto-xref">Proposition&nbsp;2</a> can also be derived from <a href="#prp-CSinR" class="quarto-xref">Proposition&nbsp;1</a> since <span class="math inline">\(\sqrt{x}\sqrt y\le (x^2 + y^2)/2\)</span> for <span class="math inline">\(x, y\ge 0\)</span>. Conversely, we may derive <a href="#prp-CSinR" class="quarto-xref">Proposition&nbsp;1</a> (even for the infinite case) from <a href="#prp-additiveIneq" class="quarto-xref">Proposition&nbsp;2</a> as well by <em>normalizing</em>. Just make the following replacements: <span class="math inline">\(a_j\to a_j\big/\sqrt{\sum_i a_i^2}\)</span> and <span class="math inline">\(b_j\to b_j\big/\sqrt{\sum_i b_i^2}\)</span>.</p>
 
 <div class="no-row-height column-margin column-container"><div class="">
 <p><em>“Normalization gives us a systematic way to pass from an additive to a multiplicative inequality.”</em></p>
@@ -942,18 +938,7 @@ <h2 class="anchored" data-anchor-id="errata">Errata</h2>
     }
     return false;
   }
-  const clipboard = new window.ClipboardJS('.code-copy-button', {
-    text: function(trigger) {
-      const codeEl = trigger.previousElementSibling.cloneNode(true);
-      for (const childEl of codeEl.children) {
-        if (isCodeAnnotation(childEl)) {
-          childEl.remove();
-        }
-      }
-      return codeEl.innerText;
-    }
-  });
-  clipboard.on('success', function(e) {
+  const onCopySuccess = function(e) {
     // button target
     const button = e.trigger;
     // don't keep focus
@@ -985,15 +970,37 @@ <h2 class="anchored" data-anchor-id="errata">Errata</h2>
     }, 1000);
     // clear code selection
     e.clearSelection();
+  }
+  const getTextToCopy = function(trigger) {
+      const codeEl = trigger.previousElementSibling.cloneNode(true);
+      for (const childEl of codeEl.children) {
+        if (isCodeAnnotation(childEl)) {
+          childEl.remove();
+        }
+      }
+      return codeEl.innerText;
+  }
+  const clipboard = new window.ClipboardJS('.code-copy-button:not([data-in-quarto-modal])', {
+    text: getTextToCopy
   });
+  clipboard.on('success', onCopySuccess);
+  if (window.document.getElementById('quarto-embedded-source-code-modal')) {
+    // For code content inside modals, clipBoardJS needs to be initialized with a container option
+    // TODO: Check when it could be a function (https://github.com/zenorocha/clipboard.js/issues/860)
+    const clipboardModal = new window.ClipboardJS('.code-copy-button[data-in-quarto-modal]', {
+      text: getTextToCopy,
+      container: window.document.getElementById('quarto-embedded-source-code-modal')
+    });
+    clipboardModal.on('success', onCopySuccess);
+  }
     var localhostRegex = new RegExp(/^(?:http|https):\/\/localhost\:?[0-9]*\//);
     var mailtoRegex = new RegExp(/^mailto:/);
       var filterRegex = new RegExp("?var:website\.site-url");
     var isInternal = (href) => {
         return filterRegex.test(href) || localhostRegex.test(href) || mailtoRegex.test(href);
     }
     // Inspect non-navigation links and adorn them if external
- 	var links = window.document.querySelectorAll('a[href]:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external):not([aria-hidden]):not(.dropdown-item):not(.quarto-navigation-tool)');
+ 	var links = window.document.querySelectorAll('a[href]:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external):not([aria-hidden]):not(.dropdown-item):not(.quarto-navigation-tool):not(.about-link)');
     for (var i=0; i<links.length; i++) {
       const link = links[i];
       if (!isInternal(link.href)) {