What $O$ -symbol supresses? I am reading this book Asymptotic Methods in Analysis by N. G. de Bruijn. It describes the definition of $O$ symbol as


  A weaker form of suppression of information is given by the 
  Bachmann-Landau O-notation. It does not suppress a function, 
  but only a number. That is to say, it replaces the knowledge of a 
  number with certain properties by the knowledge that such a 
  number exists. The O-notation suppresses much less information 
  than the limit notation, and yet it is easy enough to handle. 
  Assume that we have the following explicit information 


I don't under what does this means...

...That is to say, it replaces the knowledge of a 
number with certain properties by the knowledge that such a 
number exists...


Can anyone throw light on this passage of definition?
It will be a great help.
Thanks in Advance!
It’s trying to give an intuition and nothing more so, if the passage is not helpful to you, just skip it. Look at the actual definition instead.

Honestly, I think it’s a very bad and unhelpful attempt at giving intuition. In some ways, $\lim$ gives more information; in some ways, it gives less. In some senses, $\lim$ is more specific in that it gives a single value that the function asymptotically approaches, and the notion of limit makes sense approaching points other than $\pm\infty$.  If the limit is a real number, then saying $\lim_{n\to\infty}f(n)=c$ gives more information than $f(n)=O(1)$, which suppresses&nbsp;$c$.  

On the other hand, for many functions we're interested in, $\lim_{n\to\infty}f(n)=\infty$ so $\lim$ gives almost no information.  In those cases, big-$O$ allows you to give more information.

I wouldn’t worry about the “suppressing a number” stuff. Saying $3x=O(x)$ suppresses the number three but $3x+1=O(x)$ suppresses two numbers, $3x=O(3x)$ suppresses nothing and $x=O(3x+1)$, er, un-suppresses stuff. Somethingl ike $x=O(x^2)$ is even less clear. It's hard to tell what de Bruijn really intended.