Compactness and ContradictionAmerican Mathematical Soc., 22 במרץ 2013 - 256 עמודים There are many bits and pieces of folklore in mathematics that are passed down from advisor to student, or from collaborator to collaborator, but which are too fuzzy and nonrigorous to be discussed in the formal literature. Traditionally, it was a matter |
תוכן
Group theory | 51 |
Analysis | 79 |
NonStandard analysis | 133 |
Partial differential equations | 181 |
Miscellaneous | 217 |
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מונחים וביטויים נפוצים
abelian algebraic analogue argument arithmetic progressions asymptotic axiom basic Bayesian Bayesian probability Bolzano-Weierstrass Bolzano-Weierstrass theorem bounded bump function Cantor’s theorem Cayley graph colour compactness completion complex number computational concept constant construction contradiction coordinate correspondence principle countable counterfactual defined elementarily convergent energy equation equivalent exists exponents F-tight finitary finite formal formula function space geodesic flow geometry Gromov’s theorem group element group G Hilbert space hypothesis implies induction inequality infinite infinity input instance integers language least Lebesgue Lebesgue measure lemma limit linear lines Lipschitz mathematical metric metric space multiple natural number nilpotent non-standard analysis non-trivial nonlinear norm notation objects obtain one’s operations paradox points precisely probability measure problem proof Proposition quotient real numbers scenario sequence set theory smooth solution standard statements structure subgroup subset topology torsor triangle true ultralimit ultrapower unit vectors variable viewed zero