And exact arithmetic on Q + i*Q (complex numbers but the coordinates are rational numbers, not real numbers) is perfectly feasible.
Of course, in a real computer, long rational numbers take longer to manipulate than short rational numbers. But it's just a model. Similar to how we often assume we can handle arbitrary integers in unit time, but in reality longer integers also take longer to handle on a real computer (or we just refuse to handle them and stick to u64 only.)
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Why? It's just a model.
And exact arithmetic on Q + i*Q (complex numbers but the coordinates are rational numbers, not real numbers) is perfectly feasible.
Of course, in a real computer, long rational numbers take longer to manipulate than short rational numbers. But it's just a model. Similar to how we often assume we can handle arbitrary integers in unit time, but in reality longer integers also take longer to handle on a real computer (or we just refuse to handle them and stick to u64 only.)