Who was the first person to construct the real numbers by Cauchy sequences in $\mathbb{Q}$ Who was the first person to construct the real numbers by Cauchy sequences in $\mathbb{Q}$?
Was it Cauchy himself?

A construction of this type (though not exactly the same) is usually attributed to Cantor in 1872.  However, historians who have looked into this matter in detail note that Meray presented such a construction earlier, namely in 1869.
M´eray, H. C. R.: Remarques sur la nature des quantit´es d´efinies par la condition
de servir de limites `a des variables donn´ees, Revue des soci´eti´es savantes
des d´epartments, Section sciences math´ematiques, physiques et naturelles, 4th
ser., 10 (1869), 280–289.
For a discussion, see this article.
