To choose one sock from each of infinitely many pairs of socks requires the Axiom of choice, but for shoes the Axiom is not needed.
About this quote
- What does it mean?
- Choosing one sock from infinitely many pairs needs the axiom of choice, but picking shoes does not.
- In plain terms
- Sock selection needs the axiom of choice; shoe selection does not.
- What can you take from it?
- Mathematical principles can depend on subtle details.
Where it applies
Putting it to work
Questions to consider
- Why does the axiom matter for socks but not shoes?
- What does this reveal about infinite sets?
Another view
The analogy may oversimplify complex theory.
More from Bertrand Russell
There is much pleasure to be gained from useless knowledge.
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