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Set Theory A to Z Stats
Can you name these terms from set theory?
By
6e6f6e616d65
10m
26 Questions
73 Plays
73 Plays
73 Plays
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Score
0/26
Timer
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Hint
Answer
% Correct
The symbol for this operation resembles an upside-
down U.
intersection
84.5%
This operation on two sets yields a set containing the elements of both sets.
union
81.7%
This mathematician is regarded as the founder of set theory.
Georg Cantor
78.9%
This set is denoted with a blackboard bold Q.
rational numbers
73.2%
These numbers represent the cardinalities of infinite sets.
aleph numbers
69%
This logician showed that the continuum hypothesis cannot be disproven in ZFC. He is better known for his two 'incompleteness theorems.'
Kurt Gödel
63.4%
'For all' and 'there exists' are two of these types of entities in first order logic.
quantifiers
60.6%
This mathematician included the continuum hypothesis as the first of his namesake problems.
David Hilbert
59.2%
The above mathematician used this technique to prove that the real numbers are uncountable.
diagonalization
56.3%
This paradox shows that the axiom of choice allows a single ball to be cut into finitely many pieces and then be rearranged into two balls of equal volume to the first.
Banach-Tarski paradox
53.5%
Any set bijective to a proper subset of the natural numbers must necessarily have this property.
finiteness
53.5%
The smallest infinite one of this type of number is denoted with a lowercase omega.
ordinal numbers
53.5%
Along with Fraenkel, this man established the axioms of modern set theory.
Ernst Zermelo
53.5%
Hint
Answer
% Correct
These axioms of arithmetic can be proven from the ZFC axioms of set theory.
Peano axioms
42.3%
This webcomic by Randall Munroe includes multiple jokes about set theory.
xkcd
42.3%
Russell's paradox is a paradox in this type of set theory which does not have strict axioms.
naïve set theory
35.2%
This mathematician names a hierarchy of sets constructed using ZFC. He also developed game theory.
John von Neumann
35.2%
The axiom of choice is equivalent to Tychonoff's Theorem, which asserts the compactness of a certain type of this mathematical structure.
(product) topology
31%
This word refers to cardinals which cannot be proven to exist using the axioms of ZFC.
large cardinals
31%
The axiom of choice asserts that one of these constructions exists for every set, though many mathematicians struggle to envision an example over the real numbers.
well-ordering
28.2%
Subsets of a larger set are typically described using this notation. In this notation, a logical predicate is preceded by a vertical bar or a colon.
set-builder notation
26.8%
With ZFC, this axiom implies the continuum hypothesis, though it is independent of ZFC and the negation of the continuum hypothesis. Solvay and its namesake introduced it in 1970.
Martin's axiom
21.1%
This Penn State set theorist is the author of multiple textbooks on set theory, such as
Set Theory
and
The Axiom of Choice
.
Thomas Jech
21.1%
With Platek, this logician and philosopher created an axiom system for set theory weaker than ZFC. He also wrote an analysis of Wittgenstein's
Philosophical Investigations
.
Saul Kripke
19.7%
One of the first textbooks on set theory was
The Theory of Sets of Points
by William and his wife Grace, two mathematicians with this surname.
Young
19.7%
This David Foster Wallace book is about set theory.
Everything and More: A Compact History of Infinity
11.3%
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