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…
In: 0
we dont. **ratio**nal number means “a **ratio** of 2 integers” (like 1/2) not “a number we can rationalize about. all numbers can be rationalized about, thats kinda their thing, but some numbers like pi can never be expressed by any ratio of integers so we call them “ir**ratio**nal”.
We might use 355/113 or 3.141592654 as an approximation of pi, but pi its self can only truely be expressed as an infinite decimal. conveniently, numbers like pi and e are also able to be expressed as infinite but predictable sums (like Pi=4*(1-1/3+1/5-1/7+1/9-1/11….) ) that we can use to calculate them to any precision we feel like.
But this brings us on to infinity. infinity is NOT a number. when ever a mathmatician talks about infinity they are always cairful to say things like “as x approaches infinity” or “the number of elements is infinite”, but they never streight up “number equals infinity”
Latest Answers