is $(ℤ, <)$ a total order?

Question

I was reading about total orders on this website: https://medium.com/@WindUpDurb/on-partial-ordering-total-ordering-and-the-topological-sort-9f9c0d0d812f and they say that $(ℤ, <)$ is a total order, but I think that it's incorrect since for it to be a total order it must first be a partial order, which means the relation $<$ must be reflexive. $<$ is not reflexive, so that shouldn't be a a total order, correct?