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feat: w1 notes

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Yadunand Prem 2025-08-17 00:15:22 +08:00
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- $L_1 dot L_2 = L_1L_2 = {x y : x in L_1, y in L_2}$ - $L_1 dot L_2 = L_1L_2 = {x y : x in L_1, y in L_2}$
- $L^* = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n in NN}$ - $L^* = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n in NN}$
- $L^+ = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n gt.eq 1}$ - $L^+ = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n gt.eq 1}$
=== Proof Structure
==== Set A = Set B
1. Show $A subset.eq B$
- Take *arbitrary* element $x in A$
- Use definition of A to show $x in B$
- Therefore, $A subset.eq B$
2. Show $B subset.eq A$
- Take *arbitrary* element $x in B$
- Use definition of B to show $x in A$
- Therefore, $B subset.eq A$
3. Since $A subset.eq B$ and $B subset.eq A$, $A = B$

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cs4212/hw1-hellocaml-yadunut

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Subproject commit a976b25ebb1434189ba15627bab1720fb345f518 Subproject commit a152b7a34c9b2038b1588a3e28a5d156d41db0bf