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3 \usepackage{../langs} |
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7 \begin{document} |
7 \begin{document} |
8 \fnote{\copyright{} Christian Urban, King's College London, 2014, 2015, 2016, 2017, 2018, 2020} |
8 \fnote{\copyright{} Christian Urban, King's College London, 2014, 2015, 2016, 2017, 2018, 2020} |
9 |
9 |
230 \[ |
230 \[ |
231 \{0, 1\} \cup \{1, 2\} \cup \{4, 5\} \cup \{9, 10\} \cup |
231 \{0, 1\} \cup \{1, 2\} \cup \{4, 5\} \cup \{9, 10\} \cup |
232 \ldots |
232 \ldots |
233 \] |
233 \] |
234 |
234 |
235 \noindent but using the big union notation is more concise. |
235 \noindent but using the big union notation is more concise.\medskip |
236 |
236 |
237 As an aside: While this stuff about sets might all look trivial or |
237 As an aside: While this stuff about sets might all look trivial or |
238 even needlessly pedantic, \emph{Nature} is never simple. If you want |
238 even needlessly pedantic, \emph{Nature} is never simple. If you want |
239 to be amazed how complicated sets can get, watch out for the last |
239 to be amazed how complicated sets can get, watch out for the last |
240 lecture just before Christmas where I want to convince you of the fact |
240 lecture just before Christmas where I want to convince you of the fact |
251 $\{1, 2, 3, 4, \ldots\}$ and |
251 $\{1, 2, 3, 4, \ldots\}$ and |
252 $\{0, 1, 2, 3, 4, \ldots\}$ |
252 $\{0, 1, 2, 3, 4, \ldots\}$ |
253 \end{center} |
253 \end{center} |
254 |
254 |
255 \noindent |
255 \noindent |
256 contain actually the same amount of elements. Does this make sense? |
256 contain actually the same amount of elements. Does this make sense to you? |
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257 If yes, good. If not, then something to learn about. |
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258 |
257 Though this might all look strange, infinite sets will be a |
259 Though this might all look strange, infinite sets will be a |
258 topic that is very relevant to the material of this module. It tells |
260 topic that is very relevant to the material of this module. It tells |
259 us what we can compute with a computer (actually an algorithm) and what |
261 us what we can compute with a computer (actually an algorithm) and what |
260 we cannot. But during the first 9 lectures we can go by without this |
262 we cannot. But during the first 9 lectures we can go by without this |
261 ``weird'' stuff. End of aside.\smallskip |
263 ``weird'' stuff. End of aside.\smallskip |