TITLE: Chern classes are not numbers, are they?
QUESTION [6 upvotes]: Let $X$ be a smooth projective algebraic variety, say over $\mathbb C$. Let $E$ be a rank $r$ vector bundle on $X$. We can associate with $E$ its Chern classes $c_i(E)$. When I read "$c_i(E)$", the first thing I (automatically) do is to think where it lives. And it lives in the codimension $i$ part of the Chow ring of $X$, namely
$$
c_i(E)\in A^i(X).
$$ 
If $r>n=\dim X$, I see we can identify $c_n(E)\in A^n(X)$ with an integer. But reading some papers, I got the impression that one can do the same for the other $c_i$'s as well.
So my question is just about terminology: what does it mean, for a vector bundle $E$, to have even or odd $c_i$, if Chern classes live in $A^\ast(X)$?

REPLY [2 votes]: The only reasonable interpretation I can think of for "$c_i(E)$ is even" is that there is some class $a\in A^i(X)$ such that $c_i(E)=2a$.
However I have no interpretation for "$c_i(E)$ is odd", except the rather ridiculous one that it  means  "$c_i(E)$ is not even" ...