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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Irrational numbers effectively means you can’t represent the number with a finite number of digits using our decimal numeration system (not the literal definition). √2 is a perfectly acceptable representation for an irrational number, but you can’t represent it using decimal numeration. Is √2 “impossible for our brains to rationalize”?
If you really wanted, instead of using a base-10 number system we could use a base-√2 number system and then √2 would equal 10 exactly.
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