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by knzhou
2397 days ago
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That's true for almost any nontrivial transcendental algebraic or differential equation. Special functions to solve special cases are the norm. We could repeat the same discussion at a lower level. Suppose you tell a bright middle schooler about the basics of integration, and the power rule. Then they ask, "So what's the integral of 1/x? It can't be x^0/0..." "That's a special case. It's a function called "natural logarithm", ln(x)." "But what's the definition of that weird function?" "It's defined to be the integral of 1/x." [0] "That's pretty asinine..." [0] https://en.wikipedia.org/wiki/Natural_logarithm#Definitions |
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