How do we assign rational value to numbers like pi and infinity, numbers that mathematically have no rational ending, if our brains cannot rationalize these numbers? The concept alone is as irrational as the numbers…
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> How do we assign rational value to numbers like pi…
For pi we can approximate.
For example, we can say pi is about 3.14159.
3.14159 is a rational number, and is close enough to pi to be good enough for almost any purpose we might need it.
Infinity is a different thing entirely; in normal number theory we cannot approximate that as a rational number or really do anything with it at all. Infinity is not an irrational number, it isn’t a number at all (depending on which area of maths we are in).
It is also worth remembering that “irrational” and “rational” are just labels, with specific mathematical meanings. Like “real” and “imaginary”, they are arbitrary terms that happen to have stuck through use. There is nothing irrational in the normal sense about “irrational numbers.”
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