Econ for statists 6: Perfect competition

From my earlier discussion, Why inequality is good, part 3, I explained why a "perfectly competitive" market can happen although it is very rare. I wrote there,

In most cases, perfect competition does not exist, but in a few cases, it does. For perfect competition to occur, ALL these five factors should be present at the same time: (a) homogeneous product, (b) many sellers of a particular product, (c) many buyers of that product, (d) perfect information, and (e) free entry and exit of firms.

Take tomatoes. The small, rounded, red cherry tomatoes are different from small, not rounded (maybe flattened, oblong, etc.) tomatoes, are different from medium-size rounded tomatoes, are different from medium-size, not rounded green tomatoes, are different from large-size rounded tomatoes, are different from large, seedless tomatoes, are different from large, few seeds tomatoes, and so on.

Here, there are heterogeneous products among tomatoes alone. If we talk of perfect competition, then comparison should only be on homogenous, similar or same product in terms of quality and characteristics. Once you introduce a different product, say a different type of tomato, then one factor of perfect competition – the homogenous product criteria – is immediately violated.