diff --git a/joins.qmd b/joins.qmd
index 0f89889..25d0167 100644
--- a/joins.qmd
+++ b/joins.qmd
@@ -673,7 +673,7 @@ In equi joins the `x` keys and `y` are always equal, so we only need to show one
 We can request that dplyr keep both keys with `keep = TRUE`, leading to the code below and the re-drawn `inner_join()` in @fig-inner-both.
 
 ```{r}
-x |> left_join(y, by = "key", keep = TRUE)
+x |> inner_join(y, join_by(key == key), keep = TRUE)
 ```
 
 ```{r}
@@ -771,7 +771,7 @@ One small useful technique is to use them to restrict the cross join so that ins
 ```{r}
 df <- tibble(id = 1:4, name = c("John", "Simon", "Tracy", "Max"))
 
-df |> left_join(df, join_by(id < id))
+df |> inner_join(df, join_by(id < id))
 ```
 
 ### Rolling joins
@@ -811,6 +811,7 @@ parties <- tibble(
 Now imagine that you have a table of employee birthdays:
 
 ```{r}
+set.seed(123)
 employees <- tibble(
   name = sample(babynames::babynames$name, 100),
   birthday = ymd("2022-01-01") + (sample(365, 100, replace = TRUE) - 1)