Fixup flashcards.
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@ -176,7 +176,7 @@
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"_journal/2024-02-02.md": "a3b222daee8a50bce4cbac699efc7180",
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"_journal/2024-02-02.md": "a3b222daee8a50bce4cbac699efc7180",
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"_journal/2024-02-01.md": "3aa232387d2dc662384976fd116888eb",
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"_journal/2024-02-01.md": "3aa232387d2dc662384976fd116888eb",
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"_journal/2024-01-31.md": "7c7fbfccabc316f9e676826bf8dfe970",
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"_journal/2024-01-31.md": "7c7fbfccabc316f9e676826bf8dfe970",
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"logic/equiv-trans.md": "8bfb004bc500f32620aff7b95c0d92d7",
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"logic/equiv-trans.md": "fb7f2027b2b323374580fde8a1de579e",
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"_journal/2024-02-07.md": "8d81cd56a3b33883a7706d32e77b5889",
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"_journal/2024-02-07.md": "8d81cd56a3b33883a7706d32e77b5889",
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"algorithms/loop-invariants.md": "cbefc346842c21a6cce5c5edce451eb2",
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"algorithms/loop-invariants.md": "cbefc346842c21a6cce5c5edce451eb2",
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"algorithms/loop-invariant.md": "3b390e720f3b2a98e611b49a0bb1f5a9",
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"algorithms/loop-invariant.md": "3b390e720f3b2a98e611b49a0bb1f5a9",
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@ -252,7 +252,7 @@
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"c17/strings.md": "cd4c15b6616613d2d2458aed3053306c",
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"c17/strings.md": "cd4c15b6616613d2d2458aed3053306c",
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"c17/index.md": "78576ee41d0185df82c59999142f4edb",
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"c17/index.md": "78576ee41d0185df82c59999142f4edb",
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"c17/escape-sequences.md": "a8b99070336878b4e8c11e9e4525a500",
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"c17/escape-sequences.md": "a8b99070336878b4e8c11e9e4525a500",
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"c17/declarations.md": "29f3d23890301d7d0e023310d44540df",
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"c17/declarations.md": "3ed374b028112c554bb4ee96f9f65231",
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"algorithms/sorting/merge-sort.md": "6506483f7df6507cee0407bd205dbedd",
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"algorithms/sorting/merge-sort.md": "6506483f7df6507cee0407bd205dbedd",
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"_journal/2024-02-24.md": "9bb319d5014caf962a9ce3141076cff4",
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"_journal/2024-02-24.md": "9bb319d5014caf962a9ce3141076cff4",
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"_journal/2024-02/2024-02-23.md": "0aad297148e8cc4058b48b7e45787ca7",
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"_journal/2024-02/2024-02-23.md": "0aad297148e8cc4058b48b7e45787ca7",
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@ -274,7 +274,7 @@
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"_journal/2024-03-01.md": "a532486279190b0c12954966cbf8c3fe",
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"_journal/2024-03-01.md": "a532486279190b0c12954966cbf8c3fe",
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"_journal/2024-02/2024-02-29.md": "0e502a2c8baf90c2f12859b03f10b5a1",
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"_journal/2024-02/2024-02-29.md": "0e502a2c8baf90c2f12859b03f10b5a1",
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"algebra/sequences.md": "97c217823aacf8910a1a37bde694ecfe",
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"algebra/sequences.md": "97c217823aacf8910a1a37bde694ecfe",
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"algebra/sequences/index.md": "2385d1db23c1753f9dc744029c357283",
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"algebra/sequences/index.md": "208174a5a078b120fa11e296ad1d09c1",
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"_journal/2024-03-02.md": "08c3cae1df0079293b47e1e9556f1ce1",
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"_journal/2024-03-02.md": "08c3cae1df0079293b47e1e9556f1ce1",
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"_journal/2024-03/2024-03-01.md": "70da812300f284df72718dd32fc39322",
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"_journal/2024-03/2024-03-01.md": "70da812300f284df72718dd32fc39322",
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"algebra/sequences/triangular-numbers.md": "1ae6730fa64bbb44d1d51a899f047584",
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"algebra/sequences/triangular-numbers.md": "1ae6730fa64bbb44d1d51a899f047584",
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@ -318,7 +318,7 @@
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"_journal/2024-03/2024-03-17.md": "23f9672f5c93a6de52099b1b86834e8b",
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"_journal/2024-03/2024-03-17.md": "23f9672f5c93a6de52099b1b86834e8b",
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"set/directed-graph.md": "b4b8ad1be634a0a808af125fe8577a53",
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"set/directed-graph.md": "b4b8ad1be634a0a808af125fe8577a53",
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"set/index.md": "24a66a792b7b75329590dcfc495faa91",
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"set/index.md": "24a66a792b7b75329590dcfc495faa91",
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"set/graphs.md": "4bbcea8f5711b1ae26ed0026a4a69800",
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"set/graphs.md": "2ca3d1541345365f495657c4e6635d82",
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"_journal/2024-03-19.md": "a0807691819725bf44c0262405e97cbb",
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"_journal/2024-03-19.md": "a0807691819725bf44c0262405e97cbb",
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"_journal/2024-03/2024-03-18.md": "63c3c843fc6cfc2cd289ac8b7b108391",
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"_journal/2024-03/2024-03-18.md": "63c3c843fc6cfc2cd289ac8b7b108391",
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"awk/variables.md": "e40a20545358228319f789243d8b9f77",
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"awk/variables.md": "e40a20545358228319f789243d8b9f77",
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@ -338,7 +338,7 @@
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"x86-64/declarations.md": "75bc7857cf2207a40cd7f0ee056af2f2",
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"x86-64/declarations.md": "75bc7857cf2207a40cd7f0ee056af2f2",
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"x86-64/instructions.md": "06b7fbe1a7a9568b80239310eb72e87a",
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"x86-64/instructions.md": "06b7fbe1a7a9568b80239310eb72e87a",
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"git/refs.md": "e20c2c9b14ba6c2bd235416017c5c474",
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"git/refs.md": "e20c2c9b14ba6c2bd235416017c5c474",
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"set/trees.md": "b085bd8d08dccd8cbf02bb1b7a4baa43",
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"set/trees.md": "909c612878c863abe48c5d7b545923c8",
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"_journal/2024-03-24.md": "1974cdb9fc42c3a8bebb8ac76d4b1fd6",
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"_journal/2024-03-24.md": "1974cdb9fc42c3a8bebb8ac76d4b1fd6",
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"_journal/2024-03/2024-03-23.md": "ad4e92cc2bf37f174a0758a0753bf69b",
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"_journal/2024-03/2024-03-23.md": "ad4e92cc2bf37f174a0758a0753bf69b",
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"_journal/2024-03/2024-03-22.md": "a509066c9cd2df692549e89f241d7bd9",
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"_journal/2024-03/2024-03-22.md": "a509066c9cd2df692549e89f241d7bd9",
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"_journal/2024-05/2024-05-25.md": "3e8a0061fa58a6e5c48d12800d1ab869",
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"_journal/2024-05/2024-05-25.md": "3e8a0061fa58a6e5c48d12800d1ab869",
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"_journal/2024-05-27.md": "b36636d10eab34380f17f288868df3ae",
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"_journal/2024-05-27.md": "b36636d10eab34380f17f288868df3ae",
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"_journal/2024-05/2024-05-26.md": "abe84b5beae74baa25501c818e64fc95",
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"_journal/2024-05/2024-05-26.md": "abe84b5beae74baa25501c818e64fc95",
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"algebra/set.md": "9aadf7ca6153592b5af7e942021e56de",
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"algebra/set.md": "e3e57a0f4f15535e02adbda16bba21ed",
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"algebra/boolean.md": "ee41e624f4d3d3aca00020d9a9ae42c8",
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"algebra/boolean.md": "ee41e624f4d3d3aca00020d9a9ae42c8",
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"git/merge-conflicts.md": "761ad6137ec51d3877f7d5b3615ca5cb",
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"git/merge-conflicts.md": "761ad6137ec51d3877f7d5b3615ca5cb",
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"_journal/2024-05-28.md": "0f6aeb5ec126560acdc2d8c5c6570337",
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"_journal/2024-05-28.md": "0f6aeb5ec126560acdc2d8c5c6570337",
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"_journal/2024-06-12.md": "8cc810c0f594093768117f57461e2e9e",
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"_journal/2024-06-12.md": "8cc810c0f594093768117f57461e2e9e",
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"_journal/2024-06/2024-06-11.md": "764ccba25646673fdf7bb6a5f090394d",
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"_journal/2024-06/2024-06-11.md": "764ccba25646673fdf7bb6a5f090394d",
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"hashing/open-addressing.md": "c27e92f2865bbb426fdd1e30fc52f1ed",
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"hashing/open-addressing.md": "c27e92f2865bbb426fdd1e30fc52f1ed",
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"hashing/closed-addressing.md": "962a48517969bf5e410cf78fc584051f"
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"hashing/closed-addressing.md": "962a48517969bf5e410cf78fc584051f",
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"_journal/2024-06-13.md": "488f93abe604977d0d150070640d50c0",
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"_journal/2024-06/2024-06-12.md": "f82dfa74d0def8c3179d3d076f94558e"
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},
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},
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"fields_dict": {
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"fields_dict": {
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"Basic": [
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"Basic": [
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---
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title: "2024-06-13"
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---
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- [x] Anki Flashcards
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- [x] KoL
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- [x] OGS
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- [ ] Sheet Music (10 min.)
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- [ ] Korean (Read 1 Story)
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@ -294,8 +294,8 @@ END%%
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Basic
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Basic
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What is the result of "iterating" the following recursive definition twice? $$a_n = 3a_{n-1} + 2$$
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What is the result of "iterating" the following recursive definition twice? $$a_n = 3a_{n-1} + 2$$
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Back: $$\begin{align*}
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Back: $$\begin{align*}
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a_1 & = 3(a_0) + 2 \\
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a_1 & = 3a_0 + 2 \\
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a_2 & = 3(3(a_0) + 2) + 2
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a_2 & = 3(3a_0 + 2) + 2
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\end{align*}$$
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\end{align*}$$
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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<!--ID: 1713998412595-->
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<!--ID: 1713998412595-->
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@ -765,7 +765,7 @@ Let $A$, $B$, and $C$ be sets. If $A \neq \varnothing$,
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%%ANKI
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%%ANKI
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Basic
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Basic
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What is the left cancellation law of the Cartesian product?
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What is the left cancellation law of the Cartesian product?
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Back: $(A \times B = A \times C) \Rightarrow B = C$
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Back: If $A \neq \varnothing$ then $(A \times B = A \times C) \Rightarrow B = C$
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1718107987907-->
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<!--ID: 1718107987907-->
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END%%
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END%%
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@ -781,7 +781,7 @@ END%%
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%%ANKI
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%%ANKI
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Basic
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Basic
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What is the right cancellation law of the Cartesian product?
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What is the right cancellation law of the Cartesian product?
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Back: $(B \times A = C \times A) \Rightarrow B = C$
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Back: If $A \neq \varnothing$ then $(B \times A = C \times A) \Rightarrow B = C$
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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Reference: Herbert B. Enderton, *Elements of Set Theory* (New York: Academic Press, 1977).
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<!--ID: 1718107987928-->
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<!--ID: 1718107987928-->
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END%%
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END%%
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@ -198,9 +198,16 @@ END%%
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%%ANKI
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%%ANKI
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Cloze
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Cloze
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{1:Lower} bounds are defined on data type's numeric ranges, but not {1:upper} (except for {2:fixed-size} types).
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The C standard defines {lower} bounds on numeric ranges of data types.
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Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
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Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
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<!--ID: 1707493017244-->
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<!--ID: 1718281813453-->
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END%%
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%%ANKI
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Cloze
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The C standard does *not* define {1:upper} bounds on numeric ranges of data types (except for {1:fixed-size} types).
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Reference: Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016.
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<!--ID: 1718281813458-->
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END%%
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END%%
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## Integer Literals
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## Integer Literals
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%%ANKI
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%%ANKI
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Basic
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Basic
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What expression results from eliminating $(b; \ldots)$ notation from $(b; i{:}5)[j] = 5$?
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What propositional expression results from eliminating $(b; \ldots)$ notation from $(b; i{:}5)[j] = 5$?
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Back: $(i = j \land 5 = 5) \lor (i \neq j \land b[j] = 5)$
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Back: $(i = j \land 5 = 5) \lor (i \neq j \land b[j] = 5)$
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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Reference: Gries, David. *The Science of Programming*. Texts and Monographs in Computer Science. New York: Springer-Verlag, 1981.
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<!--ID: 1713793130095-->
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<!--ID: 1713793130095-->
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@ -262,7 +262,7 @@ END%%
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%%ANKI
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%%ANKI
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Basic
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Basic
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What does it mean for an edge to be incident from vertex $v$?
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What does it mean for an edge to be incident from vertex $v$?
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Back: $v$ is the first member of the edge.
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Back: $v$ is the first coordinate of the edge.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1710796090888-->
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<!--ID: 1710796090888-->
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END%%
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END%%
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@ -270,7 +270,7 @@ END%%
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%%ANKI
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%%ANKI
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Basic
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Basic
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What does it mean for an edge to be incident to vertex $v$?
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What does it mean for an edge to be incident to vertex $v$?
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Back: $v$ is the second member of the edge.
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Back: $v$ is the second coordinate of the edge.
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1710796090891-->
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<!--ID: 1710796090891-->
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END%%
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END%%
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%%ANKI
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%%ANKI
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Basic
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Basic
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What degrees are permitted in a full $k$-ary tree?
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What degrees are permitted in a full $k$-ary tree?
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Back: $0$ or $k$
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Back: $0$ and $k$.
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Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1713118128233-->
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<!--ID: 1713118128233-->
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END%%
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END%%
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@ -993,7 +993,7 @@ END%%
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%%ANKI
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%%ANKI
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Basic
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Basic
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What degrees are permitted in a perfect $k$-ary tree?
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What degrees are permitted in a perfect $k$-ary tree?
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Back: $0$ or $k$
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Back: $0$ and $k$.
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Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Reference: Thomas H. Cormen et al., _Introduction to Algorithms_, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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<!--ID: 1713118128234-->
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<!--ID: 1713118128234-->
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END%%
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END%%
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