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@ -327,7 +327,7 @@ Isomorphisms Between Singleton Sets
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Between any two singleton sets, we may define the only possible function.
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![The only possible function between sungletons](singleton_function.svg)
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![The only possible function between singletons](singleton_function.svg)
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The function is invertible, which means that all singleton sets are isomorphic to one another.
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Before Width: | Height: | Size: 12 KiB After Width: | Height: | Size: 12 KiB |
@ -438,9 +438,9 @@ So **True** and **False** are just the *greatest* and *least* objects of our ord
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![The whole logical system, represented as a Hasse diagram](lattice_true_false.svg)
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This is another example of the categorical concept of duality - * **True** and **False** are dual to each other*, (which makes a lot of sense if you think about it).
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This is another example of the categorical concept of duality - ***True** and **False** are dual to each other*, (which makes a lot of sense if you think about it).
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So in order to represent logic, our distributive lattice has to also be *bounded* i.e. it has to have greatest and least elements.
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So in order to represent logic, our distributive lattice has to also be *bounded* i.e. it has to have greatest and least elements (which play the roles of **True** and **False**).
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The *implies* operation
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inkscape:transform-center-x="-12.533301"
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||||
inkscape:transform-center-y="-0.84723997">
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||||
<path
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style="stroke-width:35.52600098"
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inkscape:connector-curvature="0"
|
||||
@ -265,6 +259,12 @@
|
||||
sodipodi:nodetypes="cc"
|
||||
transform="matrix(0.89574,0,0,0.81736,18.384,154.236)" />
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||||
</g>
|
||||
<circle
|
||||
cx="356.63055"
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||||
cy="86.566696"
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||||
r="18.991766"
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id="circle3389"
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style="fill:#54b948;stroke:#00873a;stroke-width:3.27335119;stroke-miterlimit:10;stroke-dasharray:none" />
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<circle
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cx="298.04181"
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cy="26.905895"
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|
Before Width: | Height: | Size: 13 KiB After Width: | Height: | Size: 13 KiB |
@ -29,6 +29,7 @@ Monoid
|
||||
Monoids
|
||||
isomorphism
|
||||
isomorphisms
|
||||
Isomorphisms
|
||||
Hasse
|
||||
Antisymmetry
|
||||
connexity
|
||||
@ -73,3 +74,9 @@ Curry-Howard-Lambek
|
||||
Curry-Howard
|
||||
Lambek
|
||||
cartesian
|
||||
functor
|
||||
functors
|
||||
Functor
|
||||
Functors
|
||||
Endofunctors
|
||||
invertible
|
||||
|
Loading…
Reference in New Issue
Block a user