See the following picture for WiFi and 3G connections.
https://picasaweb.google.com/lh/photo/UqVlC4LeMjAL6xjx4Xljfw?feat=directlink
So if the 3G is still showing, that means I'm not on Wi-Fi?
When I check the WiFi it says connected "Remembered". So that is not a way of making sure i'm connected?
To truly check, should I turn on Airplane mode? Shouldn't that work?
A picture is worth a thousand words...
Now I know that I never got hooked up to the router, as my 3G never went away. And I never got that wireless icon.