- #1

strauser

- 37

- 4

The definition of a subset can be written as:

## A \subset B \Leftrightarrow \forall x (x \in A \Rightarrow x \in B) ##

However, over which set is ##\forall## supposed to quantify? It seems to me that the two possibilities are that:

1) it quantifies over a perhaps-unmentioned universal set, of which A and B are subsets - this makes the test look like it requires a lot of

redundant work, as we certainly don't need to check elements that are not in A.

or

2) it quantifies over A, which makes the definition look clunky - why not just use the notation ##\forall x \in A(x \in B)## or similar?