From 2697f30abdd7e22d8deeeb76fdb45db54fce0318 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Abdulkadir=20Furkan=20=C5=9Eanl=C4=B1?= Date: Thu, 12 Dec 2019 16:05:24 +0100 Subject: [PATCH] Revert to hugo 0.59.1 because shit broke MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Signed-off-by: Abdulkadir Furkan Şanlı --- public/about/index.html | 13 +- public/index.html | 4 +- public/index.xml | 4 +- public/posts/eidma/index.html | 224 ++++++++++++------------ public/posts/index.html | 2 +- public/posts/index.xml | 2 +- public/tags/university-notes/index.html | 2 +- public/tags/university-notes/index.xml | 2 +- 8 files changed, 127 insertions(+), 126 deletions(-) diff --git a/public/about/index.html b/public/about/index.html index e57bb2b..545d1b3 100644 --- a/public/about/index.html +++ b/public/about/index.html @@ -6,7 +6,7 @@ - + @@ -29,7 +29,7 @@ - + @@ -38,7 +38,7 @@ - + @@ -147,16 +147,17 @@
-

+

+
  • name: Abdulkadir Furkan Şanlı
  • handle: abdulocracy
  • contact: +
    • email: my handle at disroot dot org
    • irc (freenode): abdulocracy
      • -
    -
    • +
diff --git a/public/index.html b/public/index.html index 10c1868..246b830 100644 --- a/public/index.html +++ b/public/index.html @@ -1,7 +1,7 @@ - + abdulocracy's personal site @@ -167,7 +167,7 @@
- Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. 2=7 statement x=5 not a statement In logic we do not use the equals sign, we use the equivalence sign \equiv. Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. + Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. (2=7) statement (x=5) not a statement In logic we do not use the equals sign, we use the equivalence sign (\equiv). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.
diff --git a/public/index.xml b/public/index.xml index d7702d7..0a267de 100644 --- a/public/index.xml +++ b/public/index.xml @@ -18,7 +18,7 @@ Wed, 20 Nov 2019 00:00:00 +0000 https://abdulocra.cy/posts/eidma/ - Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. 2=7 statement x=5 not a statement In logic we do not use the equals sign, we use the equivalence sign \equiv. Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. + Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. \(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. @@ -27,7 +27,7 @@ Mon, 04 Nov 2019 00:00:00 +0000 https://abdulocra.cy/about/ - name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy + name: Abdulkadir Furkan Şanlı handle: abdulocracy contact: email: my handle at disroot dot org irc (freenode): abdulocracy diff --git a/public/posts/eidma/index.html b/public/posts/eidma/index.html index 7425352..05cb824 100644 --- a/public/posts/eidma/index.html +++ b/public/posts/eidma/index.html @@ -6,7 +6,7 @@ - + @@ -29,7 +29,7 @@ - + @@ -38,7 +38,7 @@ - + @@ -161,10 +161,10 @@
  • Comes from the linguistic concept that things can be either true or false.
  • We should avoid variables when forming statements, as they may change the logical value.
      -
    • 2=7 statement
      • -
    • x=5 not a statement
      • +
    • \(2=7\) statement
      • +
    • \(x=5\) not a statement
    • -
  • In logic we do not use the equals sign, we use the equivalence sign \equiv.
    • +
  • In logic we do not use the equals sign, we use the equivalence sign \(\equiv\).
  • Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.).
  • When doing logic, we use propositional variables (e.g. p, q, r).
      @@ -172,107 +172,107 @@
  • The operations done on propositional variables are called propositional connectives.
      -
    • Conjunction: p \land q is only true if both p and q are true (0001)
      • -
    • Disjunction: p \lor q is only false if both p and q are false (0111)
      • -
    • Implication (material conditional): p \implies q is false only if p is true and q is false (truth table (1011)) +
    • Conjunction: \(p \land q\) is only true if both p and q are true \((0001)\)
      • +
    • Disjunction: \(p \lor q\) is only false if both p and q are false \((0111)\)
      • +
    • Implication (material conditional): \(p \implies q\) is false only if p is true and q is false (truth table \((1011)\))
        -
      • \equiv \neg p \lor q
        • +
      • \(\equiv \neg p \lor q\)
  • Not necessarily connectives but unary operations:
      -
    • Negation: Denoted by ~, \neg or NOT, negates the one input (10).
      • +
    • Negation: Denoted by ~, \(\neg\) or NOT, negates the one input \((10)\).
  • A (propositional) formula is a “properly constructed” logical expression.
      -
    • e.g. \neg[(p \lor q)] \land r
      • -
    • (p \land) is not a formula, as \land requires 2 variables.
      • -
    • Logical equivalence: \phi(p, q, k) \equiv \psi(p, q, k), logical value of \phi is equal to logical value of \psi.
      • -
    • Commutativity: p \land q \equiv q \land p
      • -
    • Associativity: (p \land q) \land r \equiv p \land (q \land r)
      • -
    • Distributivity: p \land (q \lor r) \equiv (p \land q) \lor (p \land r)
      • +
    • e.g. \(\neg[(p \lor q)] \land r\)
      • +
    • \((p \land)\) is not a formula, as \(\land\) requires 2 variables.
      • +
    • Logical equivalence: \(\phi(p, q, k) \equiv \psi(p, q, k)\), logical value of \(\phi\) is equal to logical value of \(\psi\).
      • +
    • Commutativity: \(p \land q \equiv q \land p\)
      • +
    • Associativity: \((p \land q) \land r \equiv p \land (q \land r)\)
      • +
    • Distributivity: \(p \land (q \lor r) \equiv (p \land q) \lor (p \land r)\)
    • Conjunctive normal form: every formula can be written as a conjunction of one or more disjunctions.
        -
      • \neg(B \lor C) can be written as \neg B \land \neg C
        • +
      • \(\neg(B \lor C)\) can be written as \(\neg B \land \neg C\)
    • -
  • Double negation law: \neg(\neg p) \equiv p
    • -

  • De Morgan’s laws: \neg(p \land q) \equiv \neg p \lor \neg q and \neg(p \lor q) \equiv \neg p \land \neg q.

    • -
  • If and only if (iff): p \iff p \equiv (p \implies q) \land (q \implies p)
    • +
  • Double negation law: \(\neg(\neg p) \equiv p\)
    • +

  • De Morgan’s laws: \(\neg(p \land q) \equiv \neg p \lor \neg q\) and \(\neg(p \lor q) \equiv \neg p \land \neg q\).

    • +
  • If and only if (iff): \(p \iff p \equiv (p \implies q) \land (q \implies p)\)
  • 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)
        • +
      • \((p \implies q) \equiv (\neg p \lor q)\)
        • +
      • \((\neg q \implies \neg p) \equiv (\neg (\neg q) \lor (\neg p) \equiv (q \lor \neg p) \equiv (\neg p \lor q)\)
  • Contradiction law:
      -
    • p \lor \neg p \equiv 1 and p \land \neg p \equiv 0
      • +
    • \(p \lor \neg p \equiv 1\) and \(p \land \neg p \equiv 0\)
    • -

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

    • +

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

    • Sets

    Quantifiers

    @@ -280,117 +280,117 @@

    Posets

    Induction

    Functions

    Combinatorics

    diff --git a/public/posts/index.html b/public/posts/index.html index 061fce0..bcd9e7a 100644 --- a/public/posts/index.html +++ b/public/posts/index.html @@ -164,7 +164,7 @@
    - Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. 2=7 statement x=5 not a statement In logic we do not use the equals sign, we use the equivalence sign \equiv. Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. + Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. (2=7) statement (x=5) not a statement In logic we do not use the equals sign, we use the equivalence sign (\equiv). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.
    diff --git a/public/posts/index.xml b/public/posts/index.xml index da049dc..737366e 100644 --- a/public/posts/index.xml +++ b/public/posts/index.xml @@ -18,7 +18,7 @@ Wed, 20 Nov 2019 00:00:00 +0000 https://abdulocra.cy/posts/eidma/ - Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. 2=7 statement x=5 not a statement In logic we do not use the equals sign, we use the equivalence sign \equiv. Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. + Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. \(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. diff --git a/public/tags/university-notes/index.html b/public/tags/university-notes/index.html index 2dd9c0d..c3a8966 100644 --- a/public/tags/university-notes/index.html +++ b/public/tags/university-notes/index.html @@ -164,7 +164,7 @@
    - Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. 2=7 statement x=5 not a statement In logic we do not use the equals sign, we use the equivalence sign \equiv. Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. + Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. (2=7) statement (x=5) not a statement In logic we do not use the equals sign, we use the equivalence sign (\equiv). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.
    diff --git a/public/tags/university-notes/index.xml b/public/tags/university-notes/index.xml index 917dc34..f8316aa 100644 --- a/public/tags/university-notes/index.xml +++ b/public/tags/university-notes/index.xml @@ -18,7 +18,7 @@ Wed, 20 Nov 2019 00:00:00 +0000 https://abdulocra.cy/posts/eidma/ - Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. 2=7 statement x=5 not a statement In logic we do not use the equals sign, we use the equivalence sign \equiv. Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc. + Mathematics without infinitely small, continuous mathematical objects. The mathematics of finite sets. Propositional calculus Comes from the linguistic concept that things can be either true or false. We should avoid variables when forming statements, as they may change the logical value. \(2=7\) statement \(x=5\) not a statement In logic we do not use the equals sign, we use the equivalence sign \(\equiv\). Logical values (booleans) are denoted by either 0 or 1 (or t, f, etc.