Is a whole cake still a "piece"

If someone eats an entire cake, is it correct to say that he ate just a piece of cake? Can a whole cake still be considered a piece of cake if consumed in one sitting?

Solution 1:

If you want to go by the dictionary definition, I think you will find agreement that piece is not the whole cake. In fact, thefreedictionary.com actually uses this phrase as an example of that definition of piece:

1. A portion or part that has been separated from a whole: a piece of cake.

Aside from the "official" definition, intuitively I think most native English speakers would agree that "I ate a piece of cake" necessarily implies that you did not eat an entire cake, because of that additional information, "a piece of". Otherwise, you would have said "I ate a cake" or "I ate cake".

The line between piece and whole is not completely clear though; for example, if someone scoops a bit of frosting with their finger, and then you eat everything else, technically you have not eaten the whole cake — does that mean you have eaten a piece? Again, I think most people would say no, but at what point, then, does it make the transition?

I imagine if you took a large group of people, and showed people pictures of cake (a full cake, 90% of a cake, 75%, half a cake, down to a sliver of cake), you would have disagreement over when you could call it a piece of cake starting from 100% to 50%, but the smaller you got, the more you'd see it called a piece. By the time you got to 50% of the cake or less I would imagine that nearly everyone would be willing to call it a piece (but as far as I know, nobody has run this experiment).

Solution 2:

A whole cake would not normally be considered a piece of cake, which has the implication that the cake was divided into slices. If, however, eating the whole cake was very easy (perhaps the cake was of excellent quality, or not very large), then eating it could perhaps be described as a "piece of cake" in the idiomatic sense. See here, meaning 9 ... http://dictionary.reference.com/browse/piece+of+cake

Solution 3:

I think this boils down to the mathematical distinction between subset (which can be the whole set) and proper subset (which must be smaller).

In common usage, the word "piece" as well as the word "subset" implies a non-empty, proper subset. People are surprised when this is not the case, even if the word is technically correct.

Confusingly enough, some items are called "piece" in common usage, even if they're not separated from a whole. For instance, "piece of candy", "piece of chocolate" (both individually produced not cut out).