Question

What is the difference between \[\subset\]and\[\subseteq\]

Answer 1

In the second one the subset can include all the elements in the first

Answer 2

Working mathematicians use both to mean the same thing.

If you want to say A is a subset of B but not equal to B, you don't use the first one because it is ambiguous. Instead you use another symbol
\[A \subsetneq B\]

For example
\[\mathbb{Q} \subsetneq \mathbb{R}\]

Answer 3

so I can say \[\mathbb{N}\subsetneq \mathbb{Z}\]

Answer 4

Yes

Answer 5

But you only have the "not equal" part if you really want to emphasize it. Otherwise just use
\[\subset\]

Answer 6

so \[\mathbb{N}\subset\mathbb{Z}\]is true anyway

Answer 7

yes

Answer 8

what other fancy letters do they have in math?
\[\mathbb{N}\mathbb{Z}\mathbb{Q}\mathbb{R}\mathbb{C}\]

Answer 9

After the ones you've listed usage really falls off. Perhaps the one used next with the highest frequency is F for a field.

Answer 10

What's a field?

Answer 11

\[\mathbb{F}\]