Flooring Tile - Install bathtub on top of ceramic tile?

I am installing a whilrpool bathtub and have built the surround but have not tiled yet.

I am wondering if I should tile up to the lip of the tub or can I set the tub lip directly onto the tile.

I am worried that if I set the tub on the tile that the tile will crack.

THe tub should be set into a base of mortar. there should be no weight on the deck or the tub can actually crack. The tub deck for tile should be framed with 2x lumber, decked with plywood and cement board set into thinset and then waterproofed with a roll on waterproofer such as Redgaurd or Blue 92 to prevent water on the tub deck from penetrating through fasteners and getting into the lumber below as it will soak right through the grout lines and into the backer, ply and framing. Of course, it could take years to cause damage, but for $30/bucket for the waterproofing, why chance it. Either tile the deck and then set the tub or shim the deck for the thickness of the tile and thinset and then tile later, sliding the tile under the tub lip. If any of the setps were not done, you can add plywood to the inside of the tub deck framing on the floor to build it up a bit more before mixing your mortar and setting your tub.