I will paste a link of a similar question asked in dsp stack exchange a month back. It clearly explains why X(0) is called the dc component and why X(0) is the summation of all the samples x[n] of the signal. 

Why is X(0) the DC component

Now for your question on how the signal can have no dc component or mean, you can make the signal mean free by subtracting the average of the signal samples from every time domain sample thereby making the signal mean free both in the time domain and frequency domain. Professor Dilip Sarwate has written a clear comment about the same in the comments section of the link i posted. 

How can a signal have no DC component
I'm playing a movement (from a Quantz flute concerto) in 2/4 time. There are reasonably lengthy passages of semiquavers with no slurs marked.

I appreciate I want to vary my articulation to make it more interesting, so how would I go about deciding where to place my slurs? Are there certain beats I shouldn't slur between because it would add emphasis in the wrong place?

Of course you can't give me a definitive answer without seeing the music, but presumably there are some general rules to follow.
