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I would like to write as a mathematical expression such sentence: x is the set of all natural numbers that can be divided by 2 without the remainder.

$\{x \in \mathbb N: What \ here? \} $

Thanks in advance, Regards, Misery

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    {x∈ℕ:$x$= 2y for all y∈ℕ }2012-05-12

1 Answers 1

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A very typical shorthand when writing the set of natural numbers divisible by $a$ is to write $a\mathbb N = \{an \in \mathbb N\;|\; n \in \mathbb N\}$. Clearly every natural number of the form $an$ where $n\in \mathbb N$ is divisible by $a$ and every such number arises in this way. This follows the usual notation for cosets.