Updated Factorials section

tommytwoeyes · Mar 29, 2016 · 46f54b2 · 46f54b2
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diff --git a/.ipynb_checkpoints/Function_Behavior_Cheatsheet-checkpoint.ipynb b/.ipynb_checkpoints/Function_Behavior_Cheatsheet-checkpoint.ipynb
@@ -24,7 +24,15 @@
    "source": [
     "## Factorials\n",
     "\n",
-    "Factorials are exceeded in growth rate by _[double exponential functions](https://en.wikipedia.org/wiki/Double_exponential_function)_ (e.g. $f(x) = e^{c^x}$) only.\n",
+    "<span style='color: orange; font-weight: bold;'>*</span>\n",
+    "Factorials are exceeded in growth rate only by _[double exponential functions](https://en.wikipedia.org/wiki/Double_exponential_function)_ (e.g. $a_n = n^n \\space \\text{or} \\space b_n = e^{x^c}$).\n",
+    "\n",
+    "$$\n",
+    "\\text{For instance, if} \\space \\{a_n\\} = \\frac{n!}{n^n} \\space \\text{, then} \\space\n",
+    "\\lim_{n\\to\\infty} \\{a_n\\} = 0\n",
+    "$$\n",
+    "\n",
+    "As $n\\to\\infty \\text{,}$ $\\{a_n\\} \\to 0$ because $n^n$ grows faster than $n!$.\n",
     "\n",
     "More details about growth rates and other data about factorials can be found on [Wikipedia](https://en.wikipedia.org/wiki/Factorial#Rate_of_growth_and_approximations_for_large_n).\n",
     "\n",

diff --git a/Function_Behavior_Cheatsheet.ipynb b/Function_Behavior_Cheatsheet.ipynb
@@ -24,7 +24,15 @@
    "source": [
     "## Factorials\n",
     "\n",
-    "Factorials are exceeded in growth rate by _[double exponential functions](https://en.wikipedia.org/wiki/Double_exponential_function)_ (e.g. $f(x) = e^{c^x}$) only.\n",
+    "<span style='color: orange; font-weight: bold;'>*</span>\n",
+    "Factorials are exceeded in growth rate only by _[double exponential functions](https://en.wikipedia.org/wiki/Double_exponential_function)_ (e.g. $a_n = n^n \\space \\text{or} \\space b_n = e^{x^c}$).\n",
+    "\n",
+    "$$\n",
+    "\\text{For instance, if} \\space \\{a_n\\} = \\frac{n!}{n^n} \\space \\text{, then} \\space\n",
+    "\\lim_{n\\to\\infty} \\{a_n\\} = 0\n",
+    "$$\n",
+    "\n",
+    "As $n\\to\\infty \\text{,}$ $\\{a_n\\} \\to 0$ because $n^n$ grows faster than $n!$.\n",
     "\n",
     "More details about growth rates and other data about factorials can be found on [Wikipedia](https://en.wikipedia.org/wiki/Factorial#Rate_of_growth_and_approximations_for_large_n).\n",
     "\n",