Geometry was arguably the first mathematical discipline developed by civilization. The need to define human property (or territory) was of utmost importance (because we don't pee on trees - well not for that reason). Knowing where the system came from can give you a greater understanding of what it means.
Geometry was arguably the first mathematical discipline developed by civilization. The need to define human property (or territory) was of utmost importance (because we don't pee on trees - well not for that reason). Knowing where the system came from can give you a greater understanding of what it means.
An astonishingly elegant technique for proving certain kinds of theorems. Originally introduced by the mathematician Georg Cantor to show that the set of real numbers is uncountable – that is, there is no one-to-one correspondence between real numbers and natural numbers, but was later found to generalize to several other contexts. Perhaps the most notable uses of this technique, in addition to Cantor's proof, are Alan Turing's answer to the Halting problem, and Gödel's proof of his famous first incompleteness theorem.
Relates the speedup of a sub-task to the resulting speedup of the whole. Trivially true, but often needed to knock down false intuition.
Used to abstract away units and fixed overhead when analyzing resource usage.
Traditional square one of theoretical computer science, with many practical applications.
Illustrates many recurring themes. Understanding the proof and usage of the pumping lemma will help you understand and apply more famous, advanced results (e.g. anything involving Turing Machines).
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