commit a911f938427ec88618b6b1507ac3929616c770f7
parent 048cb594ab336efcc9b4e2e9a3af88b4521345ed
Author: Sebastiano Tronto <sebastiano.tronto@gmail.com>
Date: Tue, 8 Sep 2020 08:41:13 +0200
Minor fixes
Diffstat:
9 files changed, 1489 insertions(+), 1161 deletions(-)
diff --git a/slides/preplogic-slides.aux b/slides/preplogic-slides.aux
@@ -70,32 +70,32 @@
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+ defining Unicode char U+00C8 (decimal 200)
+ defining Unicode char U+00C9 (decimal 201)
+ defining Unicode char U+00CA (decimal 202)
+ defining Unicode char U+00CB (decimal 203)
+ defining Unicode char U+00CC (decimal 204)
+ defining Unicode char U+00CD (decimal 205)
+ defining Unicode char U+00CE (decimal 206)
+ defining Unicode char U+00CF (decimal 207)
+ defining Unicode char U+00D0 (decimal 208)
+ defining Unicode char U+00D1 (decimal 209)
+ defining Unicode char U+00D2 (decimal 210)
+ defining Unicode char U+00D3 (decimal 211)
+ defining Unicode char U+00D4 (decimal 212)
+ defining Unicode char U+00D5 (decimal 213)
+ defining Unicode char U+00D6 (decimal 214)
+ defining Unicode char U+00D8 (decimal 216)
+ defining Unicode char U+00D9 (decimal 217)
+ defining Unicode char U+00DA (decimal 218)
+ defining Unicode char U+00DB (decimal 219)
+ defining Unicode char U+00DC (decimal 220)
+ defining Unicode char U+00DD (decimal 221)
+ defining Unicode char U+00DE (decimal 222)
+ defining Unicode char U+00DF (decimal 223)
+ defining Unicode char U+00E0 (decimal 224)
+ defining Unicode char U+00E1 (decimal 225)
+ defining Unicode char U+00E2 (decimal 226)
+ defining Unicode char U+00E3 (decimal 227)
+ defining Unicode char U+00E4 (decimal 228)
+ defining Unicode char U+00E5 (decimal 229)
+ defining Unicode char U+00E6 (decimal 230)
+ defining Unicode char U+00E7 (decimal 231)
+ defining Unicode char U+00E8 (decimal 232)
+ defining Unicode char U+00E9 (decimal 233)
+ defining Unicode char U+00EA (decimal 234)
+ defining Unicode char U+00EB (decimal 235)
+ defining Unicode char U+00EC (decimal 236)
+ defining Unicode char U+00ED (decimal 237)
+ defining Unicode char U+00EE (decimal 238)
+ defining Unicode char U+00EF (decimal 239)
+ defining Unicode char U+00F0 (decimal 240)
+ defining Unicode char U+00F1 (decimal 241)
+ defining Unicode char U+00F2 (decimal 242)
+ defining Unicode char U+00F3 (decimal 243)
+ defining Unicode char U+00F4 (decimal 244)
+ defining Unicode char U+00F5 (decimal 245)
+ defining Unicode char U+00F6 (decimal 246)
+ defining Unicode char U+00F8 (decimal 248)
+ defining Unicode char U+00F9 (decimal 249)
+ defining Unicode char U+00FA (decimal 250)
+ defining Unicode char U+00FB (decimal 251)
+ defining Unicode char U+00FC (decimal 252)
+ defining Unicode char U+00FD (decimal 253)
+ defining Unicode char U+00FE (decimal 254)
+ defining Unicode char U+00FF (decimal 255)
+ defining Unicode char U+0100 (decimal 256)
+ defining Unicode char U+0101 (decimal 257)
+ defining Unicode char U+0102 (decimal 258)
+ defining Unicode char U+0103 (decimal 259)
+ defining Unicode char U+0104 (decimal 260)
+ defining Unicode char U+0105 (decimal 261)
+ defining Unicode char U+0106 (decimal 262)
+ defining Unicode char U+0107 (decimal 263)
+ defining Unicode char U+0108 (decimal 264)
+ defining Unicode char U+0109 (decimal 265)
+ defining Unicode char U+010A (decimal 266)
+ defining Unicode char U+010B (decimal 267)
+ defining Unicode char U+010C (decimal 268)
+ defining Unicode char U+010D (decimal 269)
+ defining Unicode char U+010E (decimal 270)
+ defining Unicode char U+010F (decimal 271)
+ defining Unicode char U+0110 (decimal 272)
+ defining Unicode char U+0111 (decimal 273)
+ defining Unicode char U+0112 (decimal 274)
+ defining Unicode char U+0113 (decimal 275)
+ defining Unicode char U+0114 (decimal 276)
+ defining Unicode char U+0115 (decimal 277)
+ defining Unicode char U+0116 (decimal 278)
+ defining Unicode char U+0117 (decimal 279)
+ defining Unicode char U+0118 (decimal 280)
+ defining Unicode char U+0119 (decimal 281)
+ defining Unicode char U+011A (decimal 282)
+ defining Unicode char U+011B (decimal 283)
+ defining Unicode char U+011C (decimal 284)
+ defining Unicode char U+011D (decimal 285)
+ defining Unicode char U+011E (decimal 286)
+ defining Unicode char U+011F (decimal 287)
+ defining Unicode char U+0120 (decimal 288)
+ defining Unicode char U+0121 (decimal 289)
+ defining Unicode char U+0122 (decimal 290)
+ defining Unicode char U+0123 (decimal 291)
+ defining Unicode char U+0124 (decimal 292)
+ defining Unicode char U+0125 (decimal 293)
+ defining Unicode char U+0128 (decimal 296)
+ defining Unicode char U+0129 (decimal 297)
+ defining Unicode char U+012A (decimal 298)
+ defining Unicode char U+012B (decimal 299)
+ defining Unicode char U+012C (decimal 300)
+ defining Unicode char U+012D (decimal 301)
+ defining Unicode char U+012E (decimal 302)
+ defining Unicode char U+012F (decimal 303)
+ defining Unicode char U+0130 (decimal 304)
+ defining Unicode char U+0131 (decimal 305)
+ defining Unicode char U+0132 (decimal 306)
+ defining Unicode char U+0133 (decimal 307)
+ defining Unicode char U+0134 (decimal 308)
+ defining Unicode char U+0135 (decimal 309)
+ defining Unicode char U+0136 (decimal 310)
+ defining Unicode char U+0137 (decimal 311)
+ defining Unicode char U+0139 (decimal 313)
+ defining Unicode char U+013A (decimal 314)
+ defining Unicode char U+013B (decimal 315)
+ defining Unicode char U+013C (decimal 316)
+ defining Unicode char U+013D (decimal 317)
+ defining Unicode char U+013E (decimal 318)
+ defining Unicode char U+0141 (decimal 321)
+ defining Unicode char U+0142 (decimal 322)
+ defining Unicode char U+0143 (decimal 323)
+ defining Unicode char U+0144 (decimal 324)
+ defining Unicode char U+0145 (decimal 325)
+ defining Unicode char U+0146 (decimal 326)
+ defining Unicode char U+0147 (decimal 327)
+ defining Unicode char U+0148 (decimal 328)
+ defining Unicode char U+014A (decimal 330)
+ defining Unicode char U+014B (decimal 331)
+ defining Unicode char U+014C (decimal 332)
+ defining Unicode char U+014D (decimal 333)
+ defining Unicode char U+014E (decimal 334)
+ defining Unicode char U+014F (decimal 335)
+ defining Unicode char U+0150 (decimal 336)
+ defining Unicode char U+0151 (decimal 337)
+ defining Unicode char U+0152 (decimal 338)
+ defining Unicode char U+0153 (decimal 339)
+ defining Unicode char U+0154 (decimal 340)
+ defining Unicode char U+0155 (decimal 341)
+ defining Unicode char U+0156 (decimal 342)
+ defining Unicode char U+0157 (decimal 343)
+ defining Unicode char U+0158 (decimal 344)
+ defining Unicode char U+0159 (decimal 345)
+ defining Unicode char U+015A (decimal 346)
+ defining Unicode char U+015B (decimal 347)
+ defining Unicode char U+015C (decimal 348)
+ defining Unicode char U+015D (decimal 349)
+ defining Unicode char U+015E (decimal 350)
+ defining Unicode char U+015F (decimal 351)
+ defining Unicode char U+0160 (decimal 352)
+ defining Unicode char U+0161 (decimal 353)
+ defining Unicode char U+0162 (decimal 354)
+ defining Unicode char U+0163 (decimal 355)
+ defining Unicode char U+0164 (decimal 356)
+ defining Unicode char U+0165 (decimal 357)
+ defining Unicode char U+0168 (decimal 360)
+ defining Unicode char U+0169 (decimal 361)
+ defining Unicode char U+016A (decimal 362)
+ defining Unicode char U+016B (decimal 363)
+ defining Unicode char U+016C (decimal 364)
+ defining Unicode char U+016D (decimal 365)
+ defining Unicode char U+016E (decimal 366)
+ defining Unicode char U+016F (decimal 367)
+ defining Unicode char U+0170 (decimal 368)
+ defining Unicode char U+0171 (decimal 369)
+ defining Unicode char U+0172 (decimal 370)
+ defining Unicode char U+0173 (decimal 371)
+ defining Unicode char U+0174 (decimal 372)
+ defining Unicode char U+0175 (decimal 373)
+ defining Unicode char U+0176 (decimal 374)
+ defining Unicode char U+0177 (decimal 375)
+ defining Unicode char U+0178 (decimal 376)
+ defining Unicode char U+0179 (decimal 377)
+ defining Unicode char U+017A (decimal 378)
+ defining Unicode char U+017B (decimal 379)
+ defining Unicode char U+017C (decimal 380)
+ defining Unicode char U+017D (decimal 381)
+ defining Unicode char U+017E (decimal 382)
+ defining Unicode char U+01CD (decimal 461)
+ defining Unicode char U+01CE (decimal 462)
+ defining Unicode char U+01CF (decimal 463)
+ defining Unicode char U+01D0 (decimal 464)
+ defining Unicode char U+01D1 (decimal 465)
+ defining Unicode char U+01D2 (decimal 466)
+ defining Unicode char U+01D3 (decimal 467)
+ defining Unicode char U+01D4 (decimal 468)
+ defining Unicode char U+01E2 (decimal 482)
+ defining Unicode char U+01E3 (decimal 483)
+ defining Unicode char U+01E6 (decimal 486)
+ defining Unicode char U+01E7 (decimal 487)
+ defining Unicode char U+01E8 (decimal 488)
+ defining Unicode char U+01E9 (decimal 489)
+ defining Unicode char U+01EA (decimal 490)
+ defining Unicode char U+01EB (decimal 491)
+ defining Unicode char U+01F0 (decimal 496)
+ defining Unicode char U+01F4 (decimal 500)
+ defining Unicode char U+01F5 (decimal 501)
+ defining Unicode char U+0218 (decimal 536)
+ defining Unicode char U+0219 (decimal 537)
+ defining Unicode char U+021A (decimal 538)
+ defining Unicode char U+021B (decimal 539)
+ defining Unicode char U+0232 (decimal 562)
+ defining Unicode char U+0233 (decimal 563)
+ defining Unicode char U+1E02 (decimal 7682)
+ defining Unicode char U+1E03 (decimal 7683)
+ defining Unicode char U+200C (decimal 8204)
+ defining Unicode char U+2010 (decimal 8208)
+ defining Unicode char U+2011 (decimal 8209)
+ defining Unicode char U+2012 (decimal 8210)
+ defining Unicode char U+2013 (decimal 8211)
+ defining Unicode char U+2014 (decimal 8212)
+ defining Unicode char U+2015 (decimal 8213)
+ defining Unicode char U+2018 (decimal 8216)
+ defining Unicode char U+2019 (decimal 8217)
+ defining Unicode char U+201A (decimal 8218)
+ defining Unicode char U+201C (decimal 8220)
+ defining Unicode char U+201D (decimal 8221)
+ defining Unicode char U+201E (decimal 8222)
+ defining Unicode char U+2030 (decimal 8240)
+ defining Unicode char U+2031 (decimal 8241)
+ defining Unicode char U+2039 (decimal 8249)
+ defining Unicode char U+203A (decimal 8250)
+ defining Unicode char U+2423 (decimal 9251)
+ defining Unicode char U+1E20 (decimal 7712)
+ defining Unicode char U+1E21 (decimal 7713)
+)
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+ defining Unicode char U+00A0 (decimal 160)
+ defining Unicode char U+00A1 (decimal 161)
+ defining Unicode char U+00A3 (decimal 163)
+ defining Unicode char U+00AD (decimal 173)
+ defining Unicode char U+00B8 (decimal 184)
+ defining Unicode char U+00BF (decimal 191)
+ defining Unicode char U+00C5 (decimal 197)
+ defining Unicode char U+00C6 (decimal 198)
+ defining Unicode char U+00D8 (decimal 216)
+ defining Unicode char U+00DF (decimal 223)
+ defining Unicode char U+00E6 (decimal 230)
+ defining Unicode char U+00EC (decimal 236)
+ defining Unicode char U+00ED (decimal 237)
+ defining Unicode char U+00EE (decimal 238)
+ defining Unicode char U+00EF (decimal 239)
+ defining Unicode char U+00F8 (decimal 248)
+ defining Unicode char U+0131 (decimal 305)
+ defining Unicode char U+0141 (decimal 321)
+ defining Unicode char U+0142 (decimal 322)
+ defining Unicode char U+0152 (decimal 338)
+ defining Unicode char U+0153 (decimal 339)
+ defining Unicode char U+0174 (decimal 372)
+ defining Unicode char U+0175 (decimal 373)
+ defining Unicode char U+0176 (decimal 374)
+ defining Unicode char U+0177 (decimal 375)
+ defining Unicode char U+0218 (decimal 536)
+ defining Unicode char U+0219 (decimal 537)
+ defining Unicode char U+021A (decimal 538)
+ defining Unicode char U+021B (decimal 539)
+ defining Unicode char U+2013 (decimal 8211)
+ defining Unicode char U+2014 (decimal 8212)
+ defining Unicode char U+2018 (decimal 8216)
+ defining Unicode char U+2019 (decimal 8217)
+ defining Unicode char U+201C (decimal 8220)
+ defining Unicode char U+201D (decimal 8221)
+)
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+ defining Unicode char U+00A7 (decimal 167)
+ defining Unicode char U+00B6 (decimal 182)
+ defining Unicode char U+00B7 (decimal 183)
+ defining Unicode char U+2020 (decimal 8224)
+ defining Unicode char U+2021 (decimal 8225)
+ defining Unicode char U+2022 (decimal 8226)
)
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+ defining Unicode char U+200C (decimal 8204)
+ defining Unicode char U+2026 (decimal 8230)
+ defining Unicode char U+2122 (decimal 8482)
+ defining Unicode char U+2423 (decimal 9251)
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diff --git a/slides/preplogic-slides.pdf b/slides/preplogic-slides.pdf
Binary files differ.
diff --git a/slides/preplogic-slides.synctex.gz b/slides/preplogic-slides.synctex.gz
Binary files differ.
diff --git a/slides/preplogic-slides.tex b/slides/preplogic-slides.tex
@@ -347,15 +347,19 @@ Mathematician: ``Yes.''
Let $S$ be a set and let $A(x)$ be a ``variable statement'' that depends on
$x\in S$ (for example $S=\mathbb{N}$ and $A(x)=$``x is an even number'').
\pause
-
+ \vspace{12pt}
\begin{itemize}
\item \textbf{Universal quantifier} ($\forall$ or ``for all''):
``$\forall x\in S,\,A(x)$'' means that if we replace ``$x$'' with any
element of $S$, $A(x)$ is always \textbf{true}.
+ \vspace{9pt}
\item \textbf{Existential quantifier} ($\exists$ or ``there exists''):
``$\exists x\in S,\, A(x)$'' means that $A(x)$ is \textbf{true} for
at least one value of $x$ is $S$.
\end{itemize}
+ \vspace{12pt}
+ \pause
+ \textbf{You always need a set $S$}
\end{frame}
\begin{frame}{Quantifiers - examples}
@@ -467,8 +471,8 @@ Mathematician: ``Yes.''
\begin{enumerate}
\item Assume that there are only finitely many prime numbers.
\pause
- \item So there are $n$ prime numbers, for some number $n$.
- Call them $p_1,p_2,\dots,p_n$.
+ \item $\exists n\in \mathbb N$, there are $n$ prime numbers. Call them
+ $p_1,p_2,\dots,p_n$.
\pause
\item Let $u=p_1\times p_2\times \dots \times p_n +1$.
\pause
diff --git a/slides/preplogic-slides.toc b/slides/preplogic-slides.toc
@@ -2,4 +2,4 @@
\beamer@sectionintoc {2}{Logical operations}{11}{0}{2}
\beamer@sectionintoc {3}{Implication}{28}{0}{3}
\beamer@sectionintoc {4}{Quantifiers}{40}{0}{4}
-\beamer@sectionintoc {5}{Proofs}{46}{0}{5}
+\beamer@sectionintoc {5}{Proofs}{47}{0}{5}
