confusion between "a|b" (OR SYMBOL between letters) and "a/b" (Division Symbol between letters)

Question

I came across a notion "$b \mid a$" written in discrete mathematics book by Edward for the question "$a$ is divisible by $b$". Is this a different form of notion used in discrete mathematics?? What is the difference between "$b \mid a$" and "$b/a$". Which one should be used in which type of context because when we address $b \mid a$ here, $b$ is divisor and $a$ is dividend but it is vice-versa in $b/a$ here $a$ is divisor and $b$ is dividend if I am not wrong!

Answer 1

We can think $b|a$ as a boolean expression, i.e., it is a statement with a truth value (it is either TRUE or FALSE) whereas $b/a$ is an arithmetic operation which has a number value (when $b \ne 0$, like $1$, $1.234321, 5$, $10.5$ etc.).

On the other hand, they are related to each other. If $b|a$ is TRUE, then $a/b$ is an integer when $b \ne 0$ and $a,b \in \mathbb{Z}$.

Answer 2

b|a means that a = bc for some c, thus b is a divisor of a. It's not an operation, it just means that "b divides a" but it doesn't output any element.

a/b actually means dividing a by b, since / is an operation, and so outputs c such that a = bc