\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\newcommand{\groupMul}[1] { \cdot_{\small{#1}}}
\newcommand{\groupAdd}[1] { +_{\small{#1}}}
\newcommand{\inv}[1] {#1^{-1} }
\newcommand{\bm}[1] { \boldsymbol{#1} }
\newcommand{\qed} { {\scriptstyle \Box} }
\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Analysis::Tao::08. Infinite sets
The Continuum Hypothesis
Cantor's theorem leads to the reals having strictly larger cardinality than the natural numbers. What about sets with strictly larger cardinality to the natural numbers but strictly less than the reals?
The Continuum Hypothesis asserts that [...].
Kurt Godel and Paul Cohen separately showed that the Continuum Hypothesis is [...] other axioms of set theory; it can neither [...]
