# Month: July 2023

## 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.

## Comparing Logarithms With Different Bases

Logarithms are not hard to work with when only one base is involved (as in most real-life problems); but they can be challenging when each log has a different base. Here, we’ll look at a few problems in which we have to compare logarithms with different bases, showing various strategies.

## 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.