not necessarily, there are many HD ready tv sets that don't accept 1080p signals...in reality it's half true and half false, it really depends on the HDtv set and manufacturer.

That's funny..because no one even made that statement. 

The only totally false statement I see is where you said your 720 set runs displays at 1080p. Whether your PS3 is set to output at 1080p or 1080i, your display is not and will never be 1080p on that TV.

It will accept the signal, it displays things with said signal smaller then a 720 signal which sugests that the resolution is higher. of course it is impossible for a screen to display more pixels then it has it can however accept and display with some degree of scaling.

If its displaying in progressive or interlaced format i am not sure however it still works.

And on topic im sure the slim will support component.

yeah, that´s right. I didn´t explain myself correctly. Of course a 1280x720 panel accepts 1080p, by downgrading it usually to 1080i.

I should said hd ready don´t show a 1080p full hd signal, but convert it to a 1080i or 720p.

As a side note, the slim uses a different power connector.