Added def of set size in equiv chapter

_static/custom.js

@@ -87,6 +87,6 @@ function autoplayVideos() {
     })
 }
 
-window.addEventListener('load', autoplayVideos)
 window.addEventListener('load', addImgAnchors)
+window.addEventListener('load', autoplayVideos)
 window.addEventListener('load', addGithubLink)

dl/Equivariant.ipynb

@@ -404,7 +404,7 @@
     "\n",
     "## Converting between Space and Group\n",
     "\n",
-    "Let's see how we can convert between functions on the space $\\mathcal{X}$ and functions on the group $G$. $|G| \\geq |\\mathcal{X}|$ (because the space is homogeneous) so it is rare that we can uniquely replace each point in space with a group in $G$. Instead, we will construct a partitioning of $G$ into $|\\mathcal{X}|$ sets called a quotient space $G / H$ such that $|G / H| = |\\mathcal{X}|$. It turns out, there is a well-studied approach to arranging elements in a group called **cosets**. Constructing cosets is a two-step process. First we define a subgroup $H$. A **subgroup** means it is itself a group; it has identities and inverses. We cannot accidentally leave $H$, $h_1\\cdot{} h_2 \\in H$. For example, translation transformations are a subgroup because you cannot accidentally create a rotation when combining two translations. \n",
+    "Let's see how we can convert between functions on the space $\\mathcal{X}$ and functions on the group $G$. $|G| \\geq |\\mathcal{X}|$ ($|G|$ is number of elements) because the space is homogeneous, so it is rare that we can uniquely replace each point in space with a group in $G$. Instead, we will construct a partitioning of $G$ into $|\\mathcal{X}|$ sets called a quotient space $G / H$ such that $|G / H| = |\\mathcal{X}|$. It turns out, there is a well-studied approach to arranging elements in a group called **cosets**. Constructing cosets is a two-step process. First we define a subgroup $H$. A **subgroup** means it is itself a group; it has identities and inverses. We cannot accidentally leave $H$, $h_1\\cdot{} h_2 \\in H$. For example, translation transformations are a subgroup because you cannot accidentally create a rotation when combining two translations. \n",
     "\n",
     "```{margin}\n",
     "This process of constructing cosets and then using that to lift our function is closely related to the process of finding an induced representation on $G$ via a representation on $H$.\n",
@@ -2039,7 +2039,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.12"
+   "version": "3.8.5"
   }
  },
  "nbformat": 4,