Remark

When an abbreviating symbol $\Sigma$ is introduced, by means of a definition, to represent a certain assembly, the (usually tacit) convention is made of representing the assembly obtained by substituting an assembly $B$ for a letter $x$ in the original assembly, by the symbol obtained by the replacing the letter $x$ in $\Sigma$ by the assembly $B$ (or, more often, by an abbreviating symbol representing the assembly $B$).

¶ For example, having defined what assembly is represented by the symbol $E\otimes F$, where $E$ and $F$ are letters — an assembly which, incidentally, contains other letters besides $E$ and $F$ — the symbol $Z\otimes F$ can be used without further explanation.

¶ This rule can lead to confusions, which are avoided by the use of various typographical devices; the most common consists in replacing $x$ by $(B)$ in place of $B$.

¶ For example, $M\cap N$ denotes an assembly containing the letter $N$. If we substitute for $N$ the assembly represented by $P\cup Q$, we get an assembly denoted by $M\cap(P\cup Q)$.