# What does “cavallier extension claim” in The Algorithm Design Manual mean

I have been reading the Algorithm Design Manual by Steven S. Skienna and on page 15 it mentions a term called "cavallier extension claim" and I have been desperately trying to find a definition for this. A search in Google just returns quotes of the same book.

Possibly my confusion lies in the misspelling of the word "cavallier", which seems like it should be spelled "cavalier", unless it was the name of some French mathematician or some other concept that I am missing.

Update

As requested here is the context. First he talks about boundary errors in inductive proofs and then this:

The second and more common class of inductive proof errors concerns cavallier extension claims. Adding an extra item to a given problem instance might cause the entire optimal solution to change.

• Can you give us some context? Can you quote a few of the surrounding sentences? Maybe it just means cavalier, in the ordinary English meaning of that word. – D.W. Jun 21 '18 at 3:21
• @D.W. Good point, I added the surrounding sentences (wasn't quite sure how much I can quote before it's copyright infringement). After reviewing this a bit further I can see that this might just be the English definition along the line of "offhand", it probably isn't the nobleman. Either way, it sounds like it is something significant, but then again I couldn't find it anywhere. So any further explanation would be helpful. – ced-b Jun 21 '18 at 14:00

The phrase means "cavalier" in the ordinary English sense of the word, i.e., it is talking about a claim in a proof that is made carelessly. Without more context or examples I'm not sure exactly what pattern of flawed proof it is referring to, but it has something to do with making an assumption/claim (without justifying it) that the solution for $n+1$ is related to the solution for $n$ in a particular way.