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Omni-MATH / Let N={1,2,3,…} be the set of all positive integers, and let f be a bijection from N to N. Must there exist some positive integer n such that (f(1),f(2),…,f(n)) is a permutation of…

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Let N={1,2,3,…}\mathbb{N}=\{1,2,3, \ldots\} be the set of all positive integers, and let ff be a bijection from N\mathbb{N} to N\mathbb{N}. Must there exist some positive integer nn such that (f(1),f(2),…,f(n))(f(1), f(2), \ldots, f(n)) is a permutation of (1,2,…,n)(1,2, \ldots, n)?
Plain-text mathematical notation (without MathML)
Let N={1,2,3,…} be the set of all positive integers, and let f be a bijection from N to N. Must there exist some positive integer n such that (f(1),f(2),…,f(n)) is a permutation of (1,2,…,n)?
Original LaTeX notation
Let $\mathbb{N}=\{1,2,3, \ldots\}$ be the set of all positive integers, and let $f$ be a bijection from $\mathbb{N}$ to $\mathbb{N}$. Must there exist some positive integer $n$ such that $(f(1), f(2), \ldots, f(n))$ is a permutation of $(1,2, \ldots, n)$?

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Source and history

task_id
b78c7356-9ac4-573e-bf10-9a338567466c
task_key
test--b78c7356-9ac4-573e-bf10-9a338567466c
task_revision_id
1
config / split
/ test

Official source

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