Dense Quote by John Edensor Littlewood
“A linguist would be shocked to learn that if a set is not closed this does not mean that it is open, or again that "E is dense in E" does not mean the same thing as "E is dense in itself".”
About This Quote
Source Lecture: Mathematical Analysis, 20th century
A set not being closed does not imply it is open, and “E dense in E” differs from “E dense in itself”.
In simple terms: Closed ≠ open; density statements vary
Key Takeaway
Check definitions before assuming equivalence
Themes
mathematics
logic
set theory
Mood
analytical
precise
Type
educational
technical
When to use this quote
- teaching
- proof writing
- exam preparation
Key Concepts
topology
closure
density
Questions to Reflect On
- How do you verify set properties?
- What examples illustrate the difference?
A Different Perspective
Misinterpretation can lead to false proofs
![“I constantly meet people who are doubtful, generally without due reason, about their potential capacity [as mathematicians]. The first test is whether you got anything out of geometry. To have disliked or failed to get on with other [mathematical] subjects need mean nothing; much drill and…” quote by John Edensor Littlewood](https://sms4smile.com/quotes/img-quotes/ad0/john-edensor-littlewood-23851_born_i-constantly-meet-people-who-are-doubtfu_1210950.jpg)
