I am studying the book "What is mathematics: an elementary approach to ideas and methods" and i came over a few equations that have the single quote notation in them, and i am not sure what it mean, or even if it means different things in different context.
Here is an image of what I mean:
3 Answers
It has no special meaning here, you should just consider $a'$ being a different name from $a$ (and so possibly a different element). Another way would be writing $a_1$ and $a_2$, for example.
$a$ and $a'$ (say $a$-prime) are just two different variables. You will often find the notation used where $a'$ is related in some way to $a$ - it is a modified version of $a$, or comparable/similar in some other way.
If you see the $'$ prime mark used with a function, however, it should mean the derivative of that function: $f(x) = x^3$ and $f'(x)=3x^2$ etc, with the double prime being the second derivative, $f''(x) = 6x$.
You could have "7)" instead of "1')" etc., but if you look, the primed versions are strongly related to the unprimed versions.
