\mathbb{...}prints the enclosed text as "blackboard bold", i.e. how you would write bold letters if you had to do this on a blackboard. This can be used for uppercase letters only and usually results in vertical or near-vertical lines being doubled. On a typewriter, they would be double-struck with a small offset.\mathcal{...}prints the enclosed text in calligraphic font, giving form to the text in an expressive manner.
- For number sets such as integers or natural numbers, use
\mathbb{...}, e.g.\mathbb{Z}or\mathbb{N}. - Use
\mathcal{P}(...)for the power set of a given set, e.g.\mathcal{P}(X).