Answers

The fundamental error in the false proof that the counting numbers can be matched one-to-one with the real numbers is that, no matter how long the list of integers on the left (and their mirror reversals on the right), no number with aleph-niill digits will ever appear on each side. As a consequence no irrational decimal fraction will be listed on the right. The mirror reversals of the counting numbers, with a decimal point in front of each, form no more than a subset of the integral fractions between 0 and 1. Not even 1/3 appears in this subset because its decimal form requires aleph-null digits. In brief, all that is proved is the well-known fact that the counting numbers can be matched one-to-one with a subset of integral fractions.

The false proof reminds me of a quatrain I once perpetrated:

Pi vs e

And e is just as cursed.

I wonder: Which is larger

When their digits are reversed?

0 0

Post a comment