Is expression and its result is the same thing?

103 Views Asked by At

So, $\frac{1}{2}$ and $0.5$ are just two different ways to address the same object which is rational number $\frac{1}{2}$.

What about more complex expressions? Like $\{a, b\} \cap \{b, c\}$ is just the other way to address set $\{b\}$? Or is $\lim\limits_{x \to 0} \frac{\sin{x}}{x}$ is just a number $1$? Or is $1 + 2$ is just another way to write number $3$ and $3$ is just another way to write expression $1 + 2$?

So, Is expression and its result is the same thing?

Or little more general question: is it valid to say that an expression and all other expressions which I can get from it by applying valid operations are just different ways to address same mathematical object? Or is there a sufficient differences between writing an expression and writing an object that you can get by evaluating it in more direct way?