# Small letters to represent sets

1. Feb 2, 2010

### mousemouse

Hi,

I'd like to know if using small letters to represent sets violates rules? From what i've been taught capital letters are pretty much used to denote sets. Is this a strict rule?

2. Feb 2, 2010

### CRGreathouse

It's all about context. If I'm trying to keep sets and numbers distinct, I might use uppercase and lowercase, respectively. But I might equally well be trying to distinguish sets and proper classes, in which case I'd use lowercase for sets and uppercase for proper classes.

The goal is to use your typography to reduce the amount of effort required of the reader.

3. Feb 2, 2010

### mousemouse

Okay. In my case I did the opposite of the second item in your example. I used lowercase letters for class and uppercase for sets. I guess this would be ok. I thought there was some strict rule on the use of letters.

Thank you!

4. Feb 2, 2010

### Landau

Such a rule can't possibly be a mathematical rule. It's just convention. In axiomatic set theory, sets are often denoted by lower case letters, such as here. In 'usual mathematics', upper case letters are standard. But of course you can use whatever symbols you like. If you want to write $$\backslash^*=\{1,2\}$$, that's fine.

5. Feb 2, 2010

thanks!