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Synopsis:

\usepackage{amssymb} % in preamble ... \mathbb{uppercase-letter}

Provide blackboard bold symbols, sometimes also known as doublestruck letters, used to denote number sets such as the natural numbers, the integers, etc.

Here

\( \forall n \in \mathbb{N}, n^2 \geq 0 \)

the `\mathbb{N}`

gives blackboard bold symbol ℕ,
representing the natural numbers.

If you use other than an uppercase letter then you do not get an error but you get strange results, including unexpected characters.

There are packages that give access to symbols other than just the capital letters; look on CTAN.