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Would you write code with syntax errors and blame the compiler for not understand how smart you are, or would you just learn the language and write correct code? Your frustration shows lack of understanding and appreciation for mathematics, when in reality maths and computer science are two sides of the same coin. If you can be good at one, you can be good at the other :)

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> Would you write code with syntax errors and blame the compiler for not understand how smart you are

No, but you might tolerate example code with mild syntax errors (like using a "..." to skip unrelated material, or skipping import declarations and boilerplate to better clarify the point being made). You don't demand that every example in a programming tutorial be a fully buildable piece of software, why are you demanding that a simpified calculus tutorial exhibit full rigor?

> why are you demanding that a simpified calculus tutorial exhibit full rigor?

Aren't they just suggesting a marginal amount of rigor to communicate that the "definition" is in fact based on justifications which render it non-arbitrary?

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