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glootech t1_j6dc37u wrote

Reply to comment by unskilledplay in ELI5: Why do imaginary numbers even need to exist? by Tharsis101

You're mistaking something having a definition by being axiomatic. Imaginary unit is a construct that's a consequence of first defining natural numbers using Peano's axioms and then (in layman's terms) further "creating" other, more complex structures based on your previous results.

I agree with your other statement - imaginary numbers are just an ordinary mathematical object and there's nothing special about them. I consider real numbers to be the really, really weird ones (transcendental numbers anyone?). Imaginary numbers are just a simple extension of that weirdness. And they are also very useful, so that's a big plus.

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unskilledplay t1_j6e1oft wrote

It’s fine to call it axiomatic. You can get into that Hilbert style formalism all you want. That’s all just backwards justification of math.

There is a reason nobody picked it up and continued that work when he abandoned it.

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