Okay, but where do you get those components? Don't they need the organic matter in order to chemically extract the nutrients? If not, where do they get them?
No, you don't have to start with organic fertilizer to get fertilizer. Many components are mined from soil (sodium nitrate, mined "rock phosphate" and limestone...a calcium source, but mostly used to reduce soil acidity), while others are manufactured (some as by-products) or chemically-synthesized inorganic fertilizers. Those would include ammonium nitrate, potassium sulfate, and superphosphate, or triple superphosphate by-products.
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