I was reading universal Hashing from *Introduction to Algorithms by CLRS* and came across the following corollary regarding search,insert and delete functions on Univsersally Hashed tables 

[![enter image description here][1]][1]


 [1]: https://i.sstatic.net/go3Sd.jpg


1.How is the author able to say $n=O\left( m\right) $ ?


2. Also what does $n=O\left( m\right) $ mean ? Because $n$ is a variable and $m$ is a constant therefore the statement seems wrong 


3. Also if $n=O\left( m\right) $ is true then obviously $n=\Omega \left( m\right) $ is true thus yielding $n=\Theta \left( n\right) $