I understand that pi is the ratio of a circle\'scircumference to its diameter. S

Question

I understand that pi is the ratio of a circle'scircumference

to its diameter. Since pi is irrational, that implies that atthe

least, either the circumference or the diameter must beirrational.

I don't understand how that is possible.

 If I had a piece of string one inch long and formed it into a 

circle, couldn't I theoretically measure the diameter of that circle? 

How could that measurement be irrational? Just because I can't 

measure it accurately, it doesn't mean that the true length of it 

is some never-ending decimal. 

 So that's my question, if you understand it. Thanks.

Explanation / Answer

ahhhhhh but its that very fact that you cant find thatexact measurement that constitutes that irrationality. We as humanshave a difficult time rapping our minds around theinfinite.......thats where limits come in and help to anextent. :
There are actually more irrational numbers than rational numbers.The rationals are COUNTABLY infinite; the irrationals areUNCOUNTABLY infinite. This means that the set of irrational numbershas a cardinality called the "cardinality of the continuum," whichis strictly greater than the cardinality of the set of naturalnumbers (i.e., the set {1,2,3,4,...}). The set of rational numbershas the same cardinality (number of elements) as the set of naturalnumbers, so there are more irrationals (numbers like pi and e) thanrationals (numbers like 1/2, 3/4, etc). The squareroots of most whole numbers are irrational numbers. : It is an amazing thing , I know , that each circle no matterwhat size has a constant ratio of when comparingCircumference to diameter. This ratio of C to d is a directproportion.......with a constant of variation of . So asany variable C or d increases the other increases also but alwaysin the constant proportion of . There are infiniteamounts of irrational numbers between a given set of numbers.Almost all numbers are irrational. I know that doesnt make it anyeasier to accept but it does make for interestingconversation. : analogy of being in a pool is interesting. No matter how closeyou get to the edge, you are still in the water. : hope this helps

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