1)"add it in addition to the definition in words, rather than replace it." I did not replace the textual defenition, what I did was  "symbolic defenition " i.e:"the textual one"

2)I'll take your advice and drop the  in stating the defenition. I'had made it a standard for myself to write defenitions in this way, I forgot that this was just me. 

So check it out,( Uniform convergence ), I hope you like it this way.