This topic again

But it's not about hardware failures or anything. It's about the XBox and my tv.
I have a 42'' plasma tv, and while it didn't say "HD Ready" anywhere on the sticker on the screen when I bought it, I plugged my 360 with an HDMI cable and got 720p and 1080i options, and I get the quality picture that I would expect from a HDTV.
This leads me to believe that I have an HDTV (not full HD though). Is this correct, is my tv an HDTV? I'm thinking about buying an HD satellite receiver if it is.