Can atomicity be infinity?
Introducing the idea of "infinite atomicity" can be useful to highlight the importance of particle size on the properties of metallic or network covalent solids. As the surface to volume ratio of discrete particles becomes sufficiently large, properties of crystalline solids such as melting point, absorption wavelength and reactivity begin to diverge significantly from the limiting values observed for larger crystals. A pronounced change often occurs as the nanoparticle regime is entered, at ~$\pu{ 0.1 \mu m}$, which corresponds to ~$\pu{10^8 atoms/particle}$ or so, well short of infinity, but converging to that limit (presumably heading closer to infinite atomicity will bring you into the regime where gravitational forces become very important, but I am guessing your teacher did not mean this).

But to answer your question, I found the wikipedia useful. On network solids, it states that 


  In a network solid there are no individual molecules, and the entire crystal or amorphous solid may be considered a macromolecule.


On atomicity it provides the following comment:


  All metals and some other elements, such as carbon, do not have a simple structure but consist of a very large and indefinite number of atoms bonded together. Their atomicity cannot be determined and is usually considered as 1.