# Page 233

Location: Chapter 25, last lines of Introduction before Problem 1

## It is

... For example, suppose $X$ is the expression $S$ and $Y$ is the expression $K$. The Gödel number of $X$ is $31$ and the Gödel number of $Y$ is $24$. The expression $XY$ is $(SK)$ and its Gödel number is $3124$, which is $31 \star 24$. Now you can see the significance of the numerical operation of concatenation to the base $10$.

## It should become

... For example, suppose $X$ is the expression $S$ and $Y$ is the expression $K$. The Gödel number of $X$ is $1$ and the Gödel number of $Y$ is $2$. The expression $XY$ is $(SK)$ and its Gödel number is $3124$, which is $3 \star 1 \star 2 \star 4$. Now you can see the significance of the numerical operation of concatenation to the base $10$.

## Short explanation

Throughout Chapter 25, parentheses, generally, appear to have been reinstated explicitly: since each symbol yields a digit in the expression's Gödel number, even "obvious" parentheses make a difference. Besides, in the formal definition of term a couple of pages earlier, it is said that "given any terms $X$ and $Y$ already constructed, we may form the new term $(XY)$", the latter expression being explicitly parenthesized.

In view of this fact, it is better to explicitly observe that the symbols $S$, $K$ alone correspond to the numbers $1$ and $2$, the rest of the complete result $3124$ coming from the compulsory parentheses.