All Questions
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Is the intersection of a uncountable real numbers subset with the complemetary of a countable subset uncountable? [duplicate]
Let be $E,F\subset \Bbb{R}$ two subsets such that $E$ is uncountable and $F^c$ is countable. Is $E\cap F$ uncountable?
I guess it is true, but I am not sure since I don't see a way in order to prove ...
- 733
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0
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Is axiom of choice required to throw away repeated intervals in a constructive argument?
I am looking at this answer to this question:
Let $U \subseteq \mathbb{R}$ be open and let $x \in U$. Either $x$ is rational or irrational. If $x$ is rational, define
\begin{align}I_x = \bigcup\...
- 743
2
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0
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About Bernstein sets
Remember that a subset $X\subseteq \mathbb{R}$ is a $G_{\delta}$-set if $X$ is a countable intersection of open sets in $\mathbb{R}$. For example closed subsets of $\mathbb{R}$ are $G_{\delta}$-sets. ...
- 645
2
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Decimal expansions and topological connectedness
I'm a bit confused by the following footnote from Moschovakis's Notes on Set Theory, p. 135fn24 (in the note, $\mathcal{N}$ denotes the Baire space). The puzzling part is in bold:
One may think of $...
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