I love the way this article begins with baking jokes about Koch, Menger, and Feigen fractals. And I am avid to understand more about Cantor's work, which I think you know well enough to teach me.

Yet my understanding hangs up on a single phrase that you use a couple of times. The phrase is "consists out of" (something — in this case, intervals).

At one point you say, "… you do not end up with something that consists out of intervals." At another point you say, "although the Cantor cake is constructed by removing cake-intervals it does not consist out of intervals."

I confess I am baffled by this phrase. "Out of" can mean so many different things, and some of its meanings are opposites. When you build "out of" bricks, it means bricks were plentiful, but when you run "out of" bricks, it means bricks were lacking. And I have never before encountered the word "consists" preceding "out of."

Does "consists out of" mean the same thing as "consists of"? Or does it mean the opposite? Please forgive my failure to take your meaning. Thanks in advance for explaining!