# Definition talk:Element

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I propose to give an informal description as well as links to the definitions of some axiomatic set theories. --Inconsistency (talk) 10:35, 11 June 2015 (UTC)

- "What is a member" indeed?

- At some stage you need to get down to a level of natural language where you have to assume that the reader understands what you are talking about. If you believe that the word "member" is not adequate to define element-hood at this intuitive level, then feel free to suggest something. Link to the word in wiktionary?

- If your objection is that the treatment of elementhood is not rigorous enough, and that there needs to be a mathematical definition that rigorously defines the distinction between "within" and "outside" of a given set, then that is probably best achieved by accessing the appropriate source works on the subject in the same way that existing works have been used (see the trails of prev/next links in the Sources section).

- But it is my contention that a casual reader who knows a bit about maths should be able to find the pages for these primitive terms adequately accessible without hiding the obviousness under an avalanche of formalism. --prime mover (talk) 10:41, 11 June 2015 (UTC)

- Fair enough.

- However, I just recommended to add pages like Zermelo-Fraenkel Set Theory and links to those somewhere below "Similarly, x∉S means x is not an element of S.".

- If one wanted to use the element-relation in a proof or definition (like Definition:Subset for example) there would be a rigorous definition one could refer to. --Inconsistency (talk) 12:23, 11 June 2015 (UTC)

## Elements as Sets

This may be a silly question, but $\mathsf{Pr} \infty \mathsf{fWiki}$ uses the convention that all elements are sets right? i.e. that every element of a set is also a set? If so, then perhaps it should be mentioned in the definition. --HumblePi (talk) 20:06, 29 April 2017 (EDT)

- Not on this page it does not. The concept of an "element" is handled both in pure set theory (where all elements are themselves sets) and in non-pure set theory. $\mathsf{Pr} \infty \mathsf{fWiki}$ is more than just zfc and class theory. --prime mover (talk) 20:32, 29 April 2017 (EDT)