First rule of negotiation - never give a number
I never ever heard such a "rule". Honestly, I think you were desinformed by people like to talk from nothing until the ethernity, instead of using clear wishes and expectations.
But it really depends on the culture. As I've heard, there are regions where it is much more important to understand eachothers metacommunication, to build a "psychological bridge" between the partners. It highly depends on the country in which you live! Most answers you get here are mainly from the anglo-saxon region, but if you are in, for example, saudi arabia, maybe they won't pass your situation.
I think, you won't talk from nothing until the ethernity, while both of you try to avoid to give numbers.
Not giving a number has no real advantage, if you are with a competent partner. If your partner is incompetent, then you have some chance that he overestimates you, but it is not likely and on the longterm your life will go better if you are between competent people.
What you offer, has a market price, and it is known for both of you. In most cases, getting a little bit better price is not so important as risking to lose the whole contract.
There is another reason for that: in most cases, it is not the price what matters. If your partner thinks you (your work force) is his dream offer, he will pay for you even much more. If he thinks you are bad, he won't employ you even for a much lower wage.
The only reason to try to not give a number first: if you worth yourself much worthier as your wannabe-employer thinks, he will think you won't work well for him even if you accept his much lower offer (because you are unsatisfied).
And, if you underestimate yourself (and so say a number much lower as he would give), he will think that maybe you are not so good as you look, and this will be the reason why he won't employ you.
To defend yourself against these dangers, is not that you won't give a number, but that you know the market well.
What is really important: have clear expectations and show that you give reliable for what you were hired. You need to show that you know very well where are you on the job market, just as you will know where are you on your workplace.