I am thinking of absurdity number 3 below. I go a little further because I am amused by the well-established point with which I end this quotation.
"ABSURDITY No3 'For a price-taking firm, the demand curve for its own output is a horizontal line at the market price' (Unit 8.3)
This is false: the demand curve of a price-taking firm is not, and cannot be, horizontal: a firm supply, even if it is 'tiny', affects the price and then the demand of the good it produces.
The correct assumption should be that the firm believes that the demand curve is horizontal - an erroneous belief, but that is another story...
In their seminal article, Existence of an Equilibrium for a Competitive Economy, Kenneth Arrow and Gérard Debreu don't mention agents' beliefs but they,'...instruct each production and consumption unit to behave as if the announcement of price p were the equilibrium value' (point 1.4.1, [Benicourt's] italics)
ABSURDITY No4 All agents are price-takers (competitive equilibrium)
...Now, any reasonable person will immediately ask: if all agents are price-takers, who set[s] prices? The e-Book answers (implicitly) this question with a circular reasoning...
Conclusion: 'A competitive market', as defined in the CORE e-Book, is not 'an approximation' of any existing market. It is not:'...hard to find evidence of perfect competition' (Unit 8.3).
It is impossible.
The so-called 'competitive economy' model doesn't 'describe an idealised market structure' (Unit 8, p 44). It is not 'unrealistic' - any model is, by definition - it is irrelevant. In fact, it has nothing to do with capitalism. It can be considered, at most, as a variant of market-socialism models, with a benevolent planner setting prices, adding supplies and demands, etc." -- Emmanuelle Benicourt (2016). Is the CORE e-Book a possible solution to our problems? Real-World Economics Review, iss. no. 75, p. 135-142.