The Mudcat Café TM
Thread #152040   Message #3554732
Posted By: Airymouse
31-Aug-13 - 10:41 AM
Thread Name: BS: Who else plays little # games?
Subject: RE: BS: Who else plays little # games?
Snail. Sorry about my muddling. I meant 8 times 142857, the product to two whole numbers. The product is 1 14285 6. I isolated the first and last digits of this product, because they are the digits you have to add to get "142857".
For some psychological reason that I don't understand, people seem happy with 1/3= .333333... and 2/3= .6666666... but when you add 1/3 + 2/3 they are puzzled by 1=.9999....
Of course infinite decimals really are something different from ordinary arithmetic. You can add only two numbers at a time, so if Lewis Carroll asks what's 1 and 1 and 1 and 1, Alice should be asking herself is this ((1+1)+1) +1) or is it (1+ (1+1)) +1 or is it .... But we all know that no matter which of the possibilities Lewis has in mind the answer is 4. Putting this quibble aside finite decimals make sense .385 means 3/10 + 8/100 + 5/1000. Since you can add only two numbers at a time, no matter what order you choose you will never be able to add up the infinite list 9/10 + 9/100 + 9/1000 etc. Thus, infinite decimals are a different animal than finite decimals, which are just the finite sum of fractions.