All Things Being Practically One

I was helping Franc out with her math homework, and we somehow got to talking about pi, and how it goes on forever. Meaning, if you measure around a circle (circumference), then measure the line down the middle (diameter), and divide one by the other, you get an irrational, transcendental answer - a number that goes on forever.

Mmmmm. Pi.

That's a neat word trick, but for practical purposes, measuring things to the 39th decimal place of pi gives you a measurement accurate to the size of a hydrogen atom. Good enough for government work.

Later that night, I was teased by the thought that even for non-practical purposes, pi's value might not actually calculate, without pattern or end, to infinity. Which reminded me of a post on the Futility Closet, which proved that 0.999...∞ is the same as one. Not close to one: they have the same value.

a = 0.999…
10a = 9.999…
10a - a = 9.999… - 0.999…
9a = 9
a = 1

For all practical purposes, ceteris paribus , tat tvam asi, yar.

It's not obvious. But it is true.