I’ve never thought of real numbers as any more real (in the non-mathematical sense of the word) than other numbers, and I’ve been peeved by popularizations which use “real” and “imaginary” without making it clear that they’re using them with a specific technical meaning (e.g. stuff like “special relativity has shown that if space is real time must be imaginary, and vice versa”—yeah, they do have squares with opposite signs (though modern notation uses real 4-vectors and a non-positive-definite metric), but that’s not how a reader would be most likely to interpret that sentence).
I’ve never thought of real numbers as any more real (in the non-mathematical sense of the word) than other numbers, and I’ve been peeved by popularizations which use “real” and “imaginary” without making it clear that they’re using them with a specific technical meaning (e.g. stuff like “special relativity has shown that if space is real time must be imaginary, and vice versa”—yeah, they do have squares with opposite signs (though modern notation uses real 4-vectors and a non-positive-definite metric), but that’s not how a reader would be most likely to interpret that sentence).