As pointed out by others, subtraction is very sensitive. The following are also important examples. 1. The problem of small denominators. This is analogous to

As pointed out by others, subtraction is very sensitive. The following are also important examples. 1. The problem of small denominators. This is analogous to the subtraction issue, but it was observed and well-studied in the 19th century itself, in the context of celestial mechanics. It is fundamentally difficult to implement these numerically [1]. 2. Whenever there are algorithms which depend on a "discontinuous" choice of a pivot in order to proceed, numerical instability may follow. This is why Gaussian elimination and Gram-Schmidt orthonormalization are numerically unstable, and other algorithms like Householder transformation are preferred instead [2]. A very detailed reference on stability issues is the book by Higham [3]. Some of these are floating point issues. [1] http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=6441&option_lang=eng http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm... [2] https://en.wikipedia.org/wiki/Householder_transformation https://en.wikipedia.org/wiki/Householder_transformation [3] https://epubs.siam.org/doi/book/10.1137/1.9780898718027?mobileUi=0& https://epubs.siam.org/doi/book/10.1137/1.9780898718027?mobi...