# Zero

## Zero Factorial: Why Does 0! = 1 ?

We’ve been talking about the oddities of zero, and I want to close with another issue similar to last week’s $$0^0$$. All our questions will be essentially identical apart from details of context: “We know zero factorial equals 1; but why?” This isn’t nearly as controversial as the others, but will bring closure to the …

## Zero to the Zero Power: Indeterminate, or Defined?

Last week we looked at numbers raised to the zero power, as part of our series on oddities of zero. We’ve looked at zero divided by zero in the past, and just recently observed how 0 to the 0 power relates to degree in polynomials, which is part of the motivation for this series. But …

## Anything to the Zero Power: Why 1?

We’ve been looking at oddities of zero. Because “nothing” behaves differently than “something”, operations with it can be surprising. Although students learn that $$x^0=1$$ for any non-zero number x, they often wonder, why?? I’ve selected a few out of at least a dozen such questions in our archive.

## Is Zero Positive or Negative? Even or Odd?

Last week we looked at some basics about zero; now let’s look at whether zero is positive or negative, and then at the topic of the recent comment that triggered this series: whether zero is even or odd.

## Is Zero Really a Number?

A recent comment on the site raised questions about zero, beyond what we have discussed in the past about division by zero. Here we’ll look at basic questions about whether zero is actually a number at all, and then about multiplication by zero, which confuses a lot of people.