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From the cosmic urn of all possible functions we draw the unique random function f : X -> Y.
From the cosmic urn of all possible functions we draw the unique random function f : X -> Y.
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{| align="center" cellspacing="6" style="text-align:center; width:70%"
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<font face="courier new"><pre>
<font face="courier new"><pre>
o-----------------------------o-----------------------------o
o-----------------------------o-----------------------------o
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o-----------------------------------------------------------o
o-----------------------------------------------------------o
</pre></font>
</pre></font>
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Now we form the canonical decomposition or factorization of f into a surjective function followed by an injective function.
Now we form the canonical decomposition or factorization of f into a surjective function followed by an injective function.
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{| align="center" cellspacing="6" style="text-align:center; width:70%"
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<font face="courier new"><pre>
<font face="courier new"><pre>
o-------------------o-------------------o-------------------o
o-------------------o-------------------o-------------------o
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o-----------------------------------------------------------o
o-----------------------------------------------------------o
</pre></font>
</pre></font>
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|}
Here we have the following data:
Here we have the following data: