How many types of factors of production?

   When I was a high-school student, I was taught that there were four types of production factors, namely, land, labour, capital and entrepreneurship. I (and other students studying economics) had to learn some characteristics and properties of these four types of factors. Nowadays, DSE economics students are told, according the official syllabus, that there are three types of factors of production: human resources (labour and entrepreneurship), natural resource (land), and man-made resource (capital). Hence, these are essentially the same as what I were told during high schools, though the classification methods differ. I also quickly search the IB and GCSE AS/AL syllabus. The framework is also the basically same: there are four types of factors of production as mentioned above.
   Thus, the four (or three) types of production factors are taught to high-school students widely. Nevertheless, when students go to university, they will (sooner or later) discover that this framework is not very useful. Almost nowhere will they be told the four (or three) types again. Meanwhile, they will be told another concept: production function, which tells how output is related to inputs (factors of production). But the most common form of production function is Y = F(K,L), where Y is output, K is capital and L is labour. F(.) is nothing but the name of the mathematical function. Of course, if how K and L are related to Y is changed, then we should consider the functional form is changed, and cannot use F(.) to refer to this (new) relation (should perhaps write Y = G(K,L)). This will happen for first-year economics students, and will continue for their remaining three years.
   Well, Y = F(K,L) gives roles only to two factors, capital and labour. Where are land and entrepreneurship? Does it mean what students have learned in high schools will be considered wrong in university? Not really, but university economics also does not value very much the framework of four factors. First, land is still considered to be a factor but it is simply omitted in the production function. No economists deny the importance of land to production. But economists (especially macroeconomists) simply think that land is fixed in supply for an economy (though individual firms can acquire more lands for production but then this means another firm has fewer lands for production), and so normally the change in total output, GDP, will not be affected by the variation in land (as it does not change). You may say: this is of course not true. Total land supply increases or decreases in the real world (How to increase land supply in Hong Kong is exactly a hot topic for public discussion). Hence, we should admit that Y = F(K,L) is only a simplification of the real world situation, where sometimes it is good enough (when land is really fixed) but not always. Another treatment could be this. Although new land can be created (through, say, turning unusable lands without infrastructure into usable lands with infrastructure, or reclamation), this is mainly attributed to the capital invested in it. Thus, capital has almost taken all these effects into account. But anyway, incorporating land or not into the production is a matter of choice. There is no severe problem in principle.
   The more troublesome thing is entrepreneurship. I do not find (or have not found yet) any economics textbooks used in university take it as a factor of production. Of course, entrepreneurship is important. A firm needs someone to make decisions. There must be someone in a firm bearing the risk of investment. But is it a factor? Obviously it is not an argument in production function like Y = F(K,L). In fact, it cannot be incorporated as an argument in F(K,L). For lands, there is no problem to add it to F(K,L) so that the new model could be Y = F(K,L,N) where N is land. For entrepreneurship, you can't do this. This is because there is no clear relation between "more entrepreneurship" and "more output". In fact, we don't know how to define "more entrepreneurship".
   In (university) microeconomics, entrepreneurship (decision-maker and risk-taker) is reflected in the role of the firm owner, who conducts production plans to maximize profit, subject to production function Y = F(K,L), etc, and get the rewards (positive and negative profit). It is not a factor but a necessary agent to make any production plans realized. If anything necessary for realizing a production plan should be called a "factor" of production, then technology is also necessary. But there is no such a practice (in high school or university) to call technology as a "factor" of production. Then, why should we call entrepreneurship as a factor? If we confine "factors" to those where the quantity employed of which is directly related to output, then capital and labour (and/or lands) are factors but entrepreneurship and technology are not factors. If the relation need not be direct, then both entrepreneurship and technology can be factors, not just entrepreneurship. So, the framework of four factors, including entrepreneurship, is not very appealing. The framework using Y = F(K,L) seems to involve more consistent standard in defining what are factors.