I'm reading Burton's Elementary Number Theory (4th edition). On page 29, we read, "The number of steps in the Euclidean Algorithm usually can be reduced by selecting remainders $|r_{k+1}|<r_k/2$."
Should the $k^\mbox{th}$ remainder be enclosed by absolute value, too? In symbols, should it read $|r_{k+1}|<|r_k|/2$?