ThmDex – An index of mathematical definitions, results, and conjectures.

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Result R4213 on D77: Set union
Subresult of R2222: Set union is invariant under bijective shifting of indices

Countable set union is invariant under bijective shifting of indices

Formulation 0

Let

$X_n$ be a D11: Set for each

$n \in \mathbb{N}$ .
Let

$\pi : \mathbb{N} \to \mathbb{N}$ be a D353: Set automorphism on

$\mathbb{N}$ .

Then

$\begin{equation} \bigcup_{n \in \mathbb{N}} X_n = \bigcup_{n \in \mathbb{N}} X_{\pi(n)} \end{equation}$

Subresults

▶	R4214: Finite set union is invariant under bijective shifting of indices

Proofs

Proof 0

Let

$X_n$ be a D11: Set for each

$n \in \mathbb{N}$ .
Let

$\pi : \mathbb{N} \to \mathbb{N}$ be a D353: Set automorphism on

$\mathbb{N}$ .

$\square$