Emacs key binding for isearch-forward

Emacs key binding for isearch-forward

I'm using Emacs v24.3 on Windows 7. I'm trying to learn how to remap key
bindings.
I've created an .emacs file in my home directory and it contains one line:
(global-set-key (kbd "C-f") 'isearch-forward)
I start up Emacs with runemacs.exe. I find a non-existant file, type some
words (click at the start of the text) and type C-F to find. The I-search:
prompt displays and I can incrementally search for text. So far so go.
The problem is, if the behavior is suppose be the same as the default
isearch-forward keystroke, C-s, it isn't. When I type C-f a second time to
search for the next occurance of the string, the only thing that happens
is the I-search prompt appears in the minibuffer.
I'm not able to search for the next occurance of the string. Additionally,
the Del key is suppose to repeate the search in the reverse direction.
That does not happen for me when I search using C-f (though it does when I
search using C-s.).
So this single key mapping seems to break two things. Am I mapping wrong?
Or are these bugs? If I'm mapping wrong, how do I map C-f to the
isearch-forward command?