A question about a recipe: Not-Too-Virtuous Salad with Caramelized Apple Vinaigrette

I use one of my favorite kitchen gadgets, a Kyocera adjustable mandolin slicer, for slicing fennel. This is a very easy tool, requires no set-up, and you have a choice of four different thicknesses, so it's great for everything from garlic to cucumbers. I cut the bottom end off of the fennel and start slicing at that end, leaving the rest of it attached to the stems for storage. The second to the thickest slice, I find, is perfect for slicing fennel for salads.
http://www.amazon.com/Kyocera-CSN-202-RD-Adjustable-Mandoline-Slicer/dp/B000HZBXOA/ref=dp_cp_ob_k_title_3

Hi, AJ! I like to remove the fronds and any yucky outer pieces of the fennel, then cut the fennel in half from the frond end to the root end. Use a paring knife to remove the core. Lay the fennel half cut side down, and thinly slice perpendicular to the way you halved the fennel. If I want the pieces paper thin I'll use a veggie peeler.

Super thinly, I would use a mandolin for quickness . This one is my fave: http://www.amazon.com/gp/aw/d/B0000VZ57C/ref=redir_mdp_mobile