Arbitrary Quote by Emile Borel
![“Any argument where one supposes an arbitrary choice to be made an uncountably infinite number of times ...[is] outside the domain of mathematics.” quote by Emile Borel](https://sms4smile.com/quotes/img-quotes/70e/emile-borel-64739_arbitrary_any-argument-where-one-supposes-an-arbit_2039880.jpg)
“Any argument where one supposes an arbitrary choice to be made an uncountably infinite number of times ...[is] outside the domain of mathematics.”
About This Quote
Source Lecture: Foundations of Mathematics, 1912
Choosing an arbitrary option infinitely often exceeds mathematical rigor, making arguments ill-defined.
In simple terms: Infinite arbitrary choices are mathematically invalid.
Key Takeaway
Stay within defined mathematical domains.
Themes
mathematics
logic
philosophy
infinity
Mood
thoughtful
inquisitive
Type
philosophical
educational
When to use this quote
- formal proofs
- theoretical research
- educational curricula
Key Concepts
Set theory
countability
axiom of choice
Questions to Reflect On
- What are limits of formalism?
- How to handle infinite choices in practice?
A Different Perspective
Practical problems may require approximations beyond strict math.
