Can you use googleon and googleoff comments to prevent Googlebot from indexing part of a page?

A similar question was asked on Stack Overflow back in January.

John Mueller was kind enough to respond with the following:

"googleon" and "googleoff" are only supported by the Google Search Appliance (when you host your own search results, usually for your own internal website).

They are not supported by Google's web-search at all.

As far as I know there is no such way of telling Google not to index a element of the page.