Flooring Tile - Transition from tile to carpet

Currently there is plywood at the same level in the bathroom and adjoining bedroom. There is no threshold/etc. between the two rooms. My problem is figuring out the correct way to transition in the doorway between the two rooms.

The bathroom will have 1/2" cement board and I am assuming that I need to make it line up directly under the door between the two rooms. I have seen the metal edging that appears to get held in place by the thinset between the tiles/cement board but I don't know if I need this or not.

Any advice/links would be greatly appreciated. If something is not clear let me know and I'll try explaining it more. Thanks!!!

If you haven't installed the concrete board yet, don't use 1/2 inch. Concrete board adds no structural integrity or strength to the floor. Consequently, 1/4 inch is for floors and 1/2 inch is for walls. 1/4 inch will match up better with your carpet and make a more even transition between the two. Your assumption as to the correct termination point is correct. With the door closed, you don't want to see tile on the carpet side or carpet on the tile side. I don't personally like the metal you are referring to and don't use it in this application. I simply tuck or "stuff" the carpet to the tile, just as to a wall. If you use 1/4 inch concrete board, the two materials should end up the same height. If you use 1/2 inch concrete board, the carpet will stuff to the concrete board and the tile will be above the carpet. I like to let the tile hang out over the edge of the concrete board about an eighth of an inch to give me a place to stuff the carpet. Any more than that runs the risk of breaking the edge off the tile with traffic.

I haven't installed the cement board yet but I did cut out the one piece. Maybe I'll take the 2 uncut pieces back and get the thinner cement board. Basically I don't need a threshold then if I use the thinner board.

The 1/2" cement board adds height, weight and no strength to the floor. Smokey's right on with the 1/4" cement board.

I checked and the local lumber yard only has 3/16" and it's $16 for a 4x4 sheet instead of the $8 for the 1/2" board. Looks like I might be going out of town this weekend and picking up some thinner stuff.

Actually, most places call the 3/16 quarter inch when it's actually 3/16. I'm pretty sure the 1/4 comes in 3X4 or 3X5 sheets. One manufacturer is Durrock and one is Wonderboard. Unless I'm mistaken here, you were probably looking at Durrock.

I think the durock is actually 5/16". I havent seen 4' x4' before. Exactly what product are you looking at?