I just started a class in Number theory today and we were given a definition of what it means to say a divides b.
The definition goes as follows.
We say $b$ is a divisor of $a$ or $a$ is a multiple of $b$ if $a$ divides $b$. We write $a|b$.
But if $a$ divides $b$, doesn't this imply that $a$ is a divisor of $b$?
Also on Wikipedia it gives the opposite of what's stated in this definition https://en.wikipedia.org/wiki/Divisor.
So shouldn't the definition I stated actually read at the end
if $b$ divides $a$ we write $b|a$ ?
Yes, you are absolutely right, it should be:
We say $a$ is a divisor of $b$ or $b$ is a multiple of $a$ if $a$ divides $b.$ We write $a|b.$