# Complex, quaternions, octonions,

1. Aug 26, 2004

### quasar987

What are called the numbers with 15 imaginary part and 1 real?

And is that the limit or are there people working with numbers of more than 15 imaginary parts? If so, how many, and what's the name for them?

2. Aug 27, 2004

### Lonewolf

They're called the sedenions. Unfortunately, they do not form a division algebra (i.e. we have an a.b = 0, for a and b both not zero). We get the sedenions by performing the Cayley-Dickenson construction on octonions. We can repeat this construction as many times as we like, producing an algebra double the dimension of the previous algebra with each step.

3. Aug 27, 2004

### Alkatran

Just one of the many places where math tends towards being infinitely complicated. Oh well, means we have a lot of work ahead of us!