3 / 3 = 1. But what if I write it as ( 1 +...
. But what if I write it as or ?
Now, is a recurring/repeating/non-ending decimal so if we add these three, i.e. we will get infinitesimally close to but not
Is there a way to show that these decimals do end and will eventually become ?
Answer & Explanation
is not in the process of becoming or anything else. If it is a meaningful expression then it is already equal to or not equal to
Your Q is not trivial. A logical foundation for was only developed in the 19th century.
The decimals do not end, but that's not really a problem, since
There are several proofs of this, which you can look at yourself.
The simplest one is to say that if , then , and if you subtract the two equations you get which means
Another way is to see that