[speedplane]

There is a mathematically based definition of a perfect market. It’s only an approximation of real life, but it’s heavily used: https://www.investopedia.com/terms/p/perfectcompetition.asp

[WalterBright]

Your reference says:

"Companies earn just enough profit to stay in business"

which contradicts your comment:

"in a “perfect” market there cannot be profits"

[mhh__]

I think the idea is that in the limit T->inf the profits go to zero.