Small letters to represent sets

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Discussion Overview

The discussion revolves around the use of small letters versus capital letters to represent sets in mathematical notation. Participants explore whether there are strict rules governing this practice or if it is merely a matter of convention, considering contexts such as set theory and general mathematics.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions if using small letters for sets violates any rules, noting that capital letters are typically used for this purpose.
  • Another participant suggests that the choice between uppercase and lowercase letters depends on context, such as distinguishing between sets and numbers or sets and proper classes.
  • A different participant mentions using lowercase letters for classes and uppercase for sets, expressing uncertainty about the existence of strict rules regarding letter usage.
  • Some participants argue that there is no strict mathematical rule, asserting that it is a matter of convention and that both lowercase and uppercase letters can be used flexibly in different mathematical contexts.

Areas of Agreement / Disagreement

Participants generally agree that there are no strict rules governing the use of letter cases for sets, but multiple competing views remain regarding the conventions and contexts in which different cases should be used.

Contextual Notes

Limitations include the lack of consensus on the appropriateness of using lowercase versus uppercase letters in various mathematical contexts, as well as the dependence on specific conventions that may vary across different areas of mathematics.

mousemouse
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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?
 
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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.
 
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!
 
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 [tex]\backslash^*=\{1,2\}[/tex], that's fine.
 
Landau said:
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 [tex]\backslash^*=\{1,2\}[/tex], that's fine.

thanks!
 

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