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Limiting set of scaled natural numbers $\mathbb{N}$
This may be a non-standard question, and possibly irrelevant to the participants. Nevertheless, after reading the first chapter of Terence Tao's book on measure theory, I ended up thinking about what ...
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Is $\lim\limits_{n \to \infty} n$ "equal" to $\mathbb{N}$?
In set theory, the natural numbers are defined by means of inductive sets and the successor operation
$S(n+1) = n \cup \{n\}$
As such, we have
$1 = \{0\}$, $2 = \{0, 1\}$, $3 = \{0, 1, 2\}$, etc.
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