Abuse of notation is only a surface phenomenon. The real magic behind mathematics is in a safe and productive abuse of abstraction.
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maybe proof of existence of eigenvalue for complex vector spaces “abusing” the fundamental theorem of algebra?
It's not an abuse, is it? Just compute the characteristic polynomial, and there's always a root, ergo always an eigenvector.
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yeah it’s something mathematicians can just take for granted. but programmers can’t even assume good behaviour for floating point arithmetic
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