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work on the coding section
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lmoss committed Jan 26, 2025
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"\n",
"1. We take $\\widehat{S} = \\{\\varepsilon, \\mbox{\\tt 1}, \\mbox{\\tt 11}, \\mbox{\\tt 111}, \\ldots\\}$.\n",
"\n",
"2. $\\pi(\\mbox{\\tt 1}^n) = n$.\n",
"2. $\\pi({\\tt 1}^n) = n$.\n",
"\n",
"3. $\\widehat{0} = \\varepsilon$.\n",
"\n",
"4. ```\\widehat{s}(\\mbox{\\tt 1}^n) = \\mbox{\\tt 1}^{n+1}$.\n",
"4. ```$\\widehat{s}({\\tt 1}^n) = {\\tt 1}^{n+1}$.\n",
"\n",
"This completes the definition. There are other encodings of the same structure. For example, we could drop the empty word from $\\widehat{S}$ and adjust the rest of the encoding apparatus. We also could decide to use *binary numbers*, and even there we have several options of how to regard binary numbers as ```1#``` words.\n",
"\n",
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