From d7d4efdcbb49dd1e44169ccaa4544d0817e852c4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Abdulkadir=20Furkan=20=C5=9Eanl=C4=B1?= Date: Mon, 4 Nov 2019 16:41:08 +0100 Subject: [PATCH] Tidy up and regenerate --- content/about.md | 4 +-- content/posts/eidma.mmark | 11 +++++--- layouts/partials/extended_footer.html | 10 +++++--- layouts/partials/footer.html | 14 +++++----- public/about/index.html | 22 +++++++++------- public/categories/index.html | 22 +++++++++------- public/categories/index.xml | 2 +- public/index.html | 24 +++++++++-------- public/index.xml | 2 +- public/posts/eidma/index.html | 34 ++++++++++++++----------- public/posts/index.html | 22 +++++++++------- public/posts/index.xml | 2 +- public/sitemap.xml | 2 +- public/tags/index.html | 22 +++++++++------- public/tags/index.xml | 2 +- public/tags/university-notes/index.html | 22 +++++++++------- public/tags/university-notes/index.xml | 2 +- 17 files changed, 127 insertions(+), 92 deletions(-) diff --git a/content/about.md b/content/about.md index 10556a9..0a8ae9d 100644 --- a/content/about.md +++ b/content/about.md @@ -9,5 +9,5 @@ draft: false - name: Abdulkadir Furkan Şanlı - handle: abdulocracy - contact: - - email: my handle at disroot dot org - - irc (freenode): abdulocracy + - email: my handle at disroot dot org + - irc (freenode): abdulocracy diff --git a/content/posts/eidma.mmark b/content/posts/eidma.mmark index 945e504..809b8b0 100644 --- a/content/posts/eidma.mmark +++ b/content/posts/eidma.mmark @@ -49,12 +49,13 @@ markup = "mmark" - $$(p \implies q) \equiv (\neg p \lor q)$$ - $$(\neg q \implies \neg p) \equiv (\neg (\neg q) \lor (\neg p) \equiv (q \lor \neg p) \equiv (\neg p \lor q)$$ - - Contradiction law: - - $$p \lor \neg p \equiv 1$$ and $$p \land \neg p \equiv 0$$ +- Contradiction law: + - $$p \lor \neg p \equiv 1$$ and $$p \land \neg p \equiv 0$$ - Tautology: $$\phi (p, q, ... r)$$ is a tautology *iff* $$\phi \equiv 1$$ ## Sets + - We will consider subsets of universal set $$\mathbb X$$ - $$2^\mathbb X = \{ A : A \subseteq \mathbb X\}$$ - $$2^\mathbb X = P(\mathbb X)$$ @@ -84,12 +85,13 @@ markup = "mmark" - Quip: $$\{ x \in \mathbb R : x^2 = -1\} = \emptyset$$ ## Quantifiers + - $$\phi$$ - prepositional function: yields only true or false value - $$\forall$$ means "for all" and $$\exists$$ means "there exists" -- $$\forall$$ +- $$\forall$$: - Shorthand for $$\land$$ e.g. $$(\forall x \in \{ 1, 2, ... 10 \}) x > 0 \equiv 1 > 0 \land 2 > 0 \land ... 10 > 0$$ -- $$\exists$$ +- $$\exists$$: - Shorthand for $$\lor$$ e.g. $$(\exists x \in \{ 1, 2, ... 10 \}) x > 5 \equiv 1 > 5 \lor 2 > 5 \lor ... 10 > 5$$ - $$\neg \forall \equiv \exists$$, vice versa @@ -106,6 +108,7 @@ markup = "mmark" - Order of quantifiers matters. ## Relations + - Cartesian product: - $$A \times B = \{ (p, q) : p \in A \land q \in B \}$$ diff --git a/layouts/partials/extended_footer.html b/layouts/partials/extended_footer.html index 52cb203..0fbe96e 100644 --- a/layouts/partials/extended_footer.html +++ b/layouts/partials/extended_footer.html @@ -4,7 +4,11 @@ To add an extended footer section, please create --> - - - + diff --git a/layouts/partials/footer.html b/layouts/partials/footer.html index 8c62cf1..5590232 100644 --- a/layouts/partials/footer.html +++ b/layouts/partials/footer.html @@ -1,15 +1,16 @@ @@ -17,4 +18,3 @@ {{ partial "extended_footer.html" . }} - diff --git a/public/about/index.html b/public/about/index.html index 4db14a4..f37266a 100644 --- a/public/about/index.html +++ b/public/about/index.html @@ -165,12 +165,13 @@ @@ -180,13 +181,16 @@ - - - + - diff --git a/public/categories/index.html b/public/categories/index.html index 183bd25..03cb893 100644 --- a/public/categories/index.html +++ b/public/categories/index.html @@ -148,12 +148,13 @@ @@ -163,13 +164,16 @@ - - - + - diff --git a/public/categories/index.xml b/public/categories/index.xml index 1e679f8..b2411b5 100644 --- a/public/categories/index.xml +++ b/public/categories/index.xml @@ -1,4 +1,4 @@ - + Categories on abdulocracy's personal site diff --git a/public/index.html b/public/index.html index c2a4f9f..9489d19 100644 --- a/public/index.html +++ b/public/index.html @@ -1,7 +1,7 @@ - + abdulocracy's personal site @@ -190,12 +190,13 @@
-
- © Abdulkadir Furkan Şanlı 2019 :: CC BY-ND - - :: Theme made by panr +
+ © Abdulkadir Furkan Şanlı 2019 :: CC + BY-ND + + :: theme by panr
-
+
@@ -205,13 +206,16 @@ - - - + - diff --git a/public/index.xml b/public/index.xml index 41f0839..cfffac0 100644 --- a/public/index.xml +++ b/public/index.xml @@ -1,4 +1,4 @@ - + abdulocracy's personal site diff --git a/public/posts/eidma/index.html b/public/posts/eidma/index.html index 38ed8ab..d62cf2c 100644 --- a/public/posts/eidma/index.html +++ b/public/posts/eidma/index.html @@ -224,19 +224,19 @@

  • Contraposition law:

      -

    • \((p \implies q) \equiv (\neg q \implies \neg p)\) prove by contraposition

      +
    • \((p \implies q) \equiv (\neg q \implies \neg p)\) prove by contraposition
      • \((p \implies q) \equiv (\neg p \lor q)\)
      • \((\neg q \implies \neg p) \equiv (\neg (\neg q) \lor (\neg p) \equiv (q \lor \neg p) \equiv (\neg p \lor q)\)
      • +

  • Contradiction law:

    • \(p \lor \neg p \equiv 1\) and \(p \land \neg p \equiv 0\)
    • -

  • Tautology: \(\phi (p, q, ... r)\) is a tautology iff \(\phi \equiv 1\)

    • @@ -297,16 +297,16 @@
  • \(\phi\) - prepositional function: yields only true or false value
  • \(\forall\) means "for all" and \(\exists\) means "there exists"
    • -

  • \[\forall\]

    +

  • \(\forall\):

      -
    • Shorthand for \[\land\] e.g. \[(\forall x \in \{ 1, 2, ... 10 \}) x > 0 \equiv 1 > 0 \land 2 > 0 \land ... 10 > 0\]
      • +
    • Shorthand for \(\land\) e.g. \((\forall x \in \{ 1, 2, ... 10 \}) x > 0 \equiv 1 > 0 \land 2 > 0 \land ... 10 > 0\)
    • -

  • \[\exists\]

    +

  • \(\exists\):

      -
    • Shorthand for \[\lor\] e.g. \[(\exists x \in \{ 1, 2, ... 10 \}) x > 5 \equiv 1 > 5 \lor 2 > 5 \lor ... 10 > 5\]
      • +
    • Shorthand for \(\lor\) e.g. \((\exists x \in \{ 1, 2, ... 10 \}) x > 5 \equiv 1 > 5 \lor 2 > 5 \lor ... 10 > 5\)

  • \(\neg \forall \equiv \exists\), vice versa

    • @@ -399,12 +399,13 @@
    -
    - © Abdulkadir Furkan Şanlı 2019 :: CC BY-ND - - :: Theme made by panr +
    + © Abdulkadir Furkan Şanlı 2019 :: CC + BY-ND + + :: theme by panr
    -
    +
    @@ -414,13 +415,16 @@ - - - + - diff --git a/public/posts/index.html b/public/posts/index.html index a0dea29..d8e25eb 100644 --- a/public/posts/index.html +++ b/public/posts/index.html @@ -187,12 +187,13 @@
    -
    - © Abdulkadir Furkan Şanlı 2019 :: CC BY-ND - - :: Theme made by panr +
    + © Abdulkadir Furkan Şanlı 2019 :: CC + BY-ND + + :: theme by panr
    -
    +
    @@ -202,13 +203,16 @@ - - - + - diff --git a/public/posts/index.xml b/public/posts/index.xml index 29e8146..92284c9 100644 --- a/public/posts/index.xml +++ b/public/posts/index.xml @@ -1,4 +1,4 @@ - + Posts on abdulocracy's personal site diff --git a/public/sitemap.xml b/public/sitemap.xml index fa5d90e..d4f094a 100644 --- a/public/sitemap.xml +++ b/public/sitemap.xml @@ -1,4 +1,4 @@ - + diff --git a/public/tags/index.html b/public/tags/index.html index d989041..b6a17a4 100644 --- a/public/tags/index.html +++ b/public/tags/index.html @@ -148,12 +148,13 @@
    -
    - © Abdulkadir Furkan Şanlı 2019 :: CC BY-ND - - :: Theme made by panr +
    + © Abdulkadir Furkan Şanlı 2019 :: CC + BY-ND + + :: theme by panr
    -
    +
    @@ -163,13 +164,16 @@ - - - + - diff --git a/public/tags/index.xml b/public/tags/index.xml index 270dc20..cc3798b 100644 --- a/public/tags/index.xml +++ b/public/tags/index.xml @@ -1,4 +1,4 @@ - + Tags on abdulocracy's personal site diff --git a/public/tags/university-notes/index.html b/public/tags/university-notes/index.html index ce03eac..9715d77 100644 --- a/public/tags/university-notes/index.html +++ b/public/tags/university-notes/index.html @@ -187,12 +187,13 @@
    -
    - © Abdulkadir Furkan Şanlı 2019 :: CC BY-ND - - :: Theme made by panr +
    + © Abdulkadir Furkan Şanlı 2019 :: CC + BY-ND + + :: theme by panr
    -
    +
    @@ -202,13 +203,16 @@ - - - + - diff --git a/public/tags/university-notes/index.xml b/public/tags/university-notes/index.xml index 06a3a85..67901f1 100644 --- a/public/tags/university-notes/index.xml +++ b/public/tags/university-notes/index.xml @@ -1,4 +1,4 @@ - + university-notes on abdulocracy's personal site