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In ZFC, do we use the set $\mathbb{N}$ in the definition of $\mathbb{N}$ recursively?
In ZFC set theory, we define the set of the natural numbers as follows: By the axiom of infinity, an inductive set exists. Let I be an inductive set. Then, $\mathbb{N}$ is defined as $\{ x\in I |\...
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Is natural numbers set $\mathbb N$ infinite set?
A set with uncountable number of elements is called an infinite set.
Is that the set of all natural numbers, $\Bbb N=\text{{$1,2,3,\ldots$}}$ infinite set?
As far i know $\Bbb N$ is "countably" ...
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Is this a correct definition of the natural numbers in ZF?
Set $s$ is a natural number if $s$ is transitive and for every $x$, $y$ and $z$
$y\in{s}\rightarrow(y$ is transitive$)$, and if
$x\in{P}s\wedge(x$ is transitive$)\wedge{z}\in{P}x\wedge(z$ is ...
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