In his Cours d'analyse of 1821, Cauchy "proved" that if a sum of continuous functions converges pointwise, then its limit is also continuous.
Cauchy (1821) kekeh saking tes konvergensi sane ketat, ia nyinahang wantah yening kalih deret konvergen, produk ipun durung sakadi kenten, lan antuk ia ngawitin patemon kriteria sane efektif.