How can we use irrational numbers in math if we don’t know the full number?
In: 232
These answers are all entirely missing the point.
To illustrate, try the number
0.1234567891011121314…
Its irrational as you can get (transcendental and normal), and yet I don’t think you’d argue that we don’t “fully know the number”.
In general, for (computable) irrational numbers, we *do* know the full number. The fact that we cannot faithfully represent an irrational number in decimal notation doesn’t mean we “don’t know the full number”, it means decimal notation is an awfully inconvenient way to represent irrational numbers.
Zooming out further, it’s unclear to me why the symbols √2 or π are any less “exact” than the symbols 3, or 7/4. Each of those symbols specify a unique real number. Again, it’s true that in decimal notation irrational numbers cannot be captured by a finite string of digits, but base notation is a fairly artificial way of representing a number, so this doesn’t say much about the fundamental nature of irrational numbers.
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