A bit about zero

20 December 2009

I got up this morning with the intention of writing a bit about zero, but first I checked Twitter and came across the following tweet.

@RepublicOfMath I thought I had 3 apples, but I counted them; 0,1,2 and only had 2. RT @toddlee @t_uda retweet if we think 0 is a natural number?

I do something similar during class, but I use my fingers instead of apples.

I woke up this morning and decided to make sure I had all my fingers… 0, 1, 2, 3, 4… Doh! I’m missing a finger!

I (@MathBabbler) replied to the @RepublicOfMath tweet with the following tweet.

In the computing world, 0 is a natural number. It’s been the cause of many off-by-one errors.

Now… back to the bit I wanted to write about zero.

Add 0 to a quantity and the quantity remains unchanged; subtract 0 from a quantity and the quantity remains unchanged. But, multiply a quantity by zero and it becomes zero. Divide a quantity by zero and run the risk of crashing a computer. It’s okay to take nothing and divide-by something, but don’t even think about dividing something by nothing.

This almost as destructive as multiplying by zero: Raise a non-zero quantity to the power of zero and get one.

Zero factorial (written 0!) is one. What a great power of zero example: Take nothing (i.e. zero) and turn it into something (i.e. one). I wish I could factorialize all the zero pennies I have.

Zero is cool because it’s both a digit and a number. Plus, it is a digit in every number system from base-2 (binary) on up.

Zero is neither positive nor negative, yet +0 typically implies you have a positive quantity that is so small that it might was well be zero and -0 implies you have a negative quantity that is so close to zero that for all practical purposes its zero.

Is zero even or odd? Many consider it even, yet it’s odd to do arithmetic with it.