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lmoss committed Jan 24, 2025
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18 changes: 7 additions & 11 deletions introOneSharp/functions.ipynb
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},
"source": [
"\n",
"At this point we know what programs of ```111``` are and how they work.\n",
"At this point we know what programs of ```1#``` are and how they work.\n",
"We are interested not just in the programs themselves\n",
"but in *what* they compute. \n",
"\n",
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]
},
{
"attachments": {},
"cell_type": "markdown",
"metadata": {
"id": "ZhaXDhZfFra5"
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" \n",
"For other programs $q$ there might be some programs $p$ for which $\\phifn_p$ is defined for some but not all input words. \n",
"\n",
"\n",
"\n",
"```{admonition} Definition\n",
":class: tip\n",
"```{prf:definition}\n",
"\n",
"Given words $x$ and $y$, we write\n",
"\n",
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"\n",
"\n",
"```{prf:definition}\n",
"\\:class: tip\n",
":class: tip\n",
"\n",
"Every word $p$ gives us a function\n",
"called $\\phifn^n_p$ on $n$-tuples of words. \n",
"\n",
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"cell_type": "markdown",
"metadata": {},
"source": [
"```{admonition} Definition\n",
":class: tip\n",
"```{prf:definition}\n",
"$$\n",
"\\phifn^0_p (\\ ) \\simeq y\n",
"$$\n",
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"id": "ZkwdFYl1iXHH"
},
"source": [
"\n",
"```{admonition} Definition\n",
":class: tip\n",
"```{prf:definition} \n",
"For any set $A$, the *characteristic function of $A$* is the function $\\chi_A$ given by\n",
"\n",
"$$\n",
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