Tinsology

I suddenly recall something interesting a professor of mine pointed out a couple years ago while on a tangent during lecture. It has to do with the nature of infinity and how accepting something perfectly reasonable as true leads to less intuitive, but equally true conclusions.

The following expression is true and most people would not argue otherwise:

1/3 = .3333333333 . . .


Assume, of course, that there is an infinite number of 3s trailing the decimal point. The following expression is also true, and even fewer people would argue otherwise:


1/3 + 1/3 + 1/3 = 1


This may seem obvious, but what may be less obvious is what follows logically from the two expressions above:

  .333333 . . .
  .333333 . . .
+ .333333 . . .
_______________________
  .999999 . . .  =  1

You may be reluctant to accept that the third expression is true, but if you accept the first two expressions, there is no avoiding it. Most people with a background in computer science or mathematics probably won’t be blown away by this, but it is fun, nerdy thing to point out to your friends in the humanities department (or anyone with a B.A.)