Определенные артикли перед существительными, которые однозначно определены контекстом в момент использования

Let us consider the equation $y=ax+b$

Let $x$ be the root of equation (1) (если (1) имеет единственный корень)

Let $T$ be the linear transformation defined by (1) (если оно единственно)

We see that $x=1$ in the compact set $X$ of all points at distance 1 from $A$

Let $B$ be the Banach space of all linear operators in $X$

Let $A=B$ under the usual boundary conditions

This notation is introduced with the natural definitions of addition and multiplication

Using the standard inner (scalar, dot) product, we may (can) conclude that $Ax=0$