Re:All Horses Are the Same Color
by mannerheim on Monday December 06, 2021 @06:28PM
(#29467134)
There are several 'mathematical' ways you could phrase it (glossing over how to define the colour of a horse):
1) In a set of horses with size n, if horses A and B being both members of this set implies horse A has the same colour as horse B, then all horses in the set have the same colour.
2) In a set of horses with size n, and let f be a function on this set that produces each horse's colour. Then all horses in this set have the same colour if and only if the codomain of f on this set has size 1.
You could probably prove these are equivalent definitions.
1) In a set of horses with size n, if horses A and B being both members of this set implies horse A has the same colour as horse B, then all horses in the set have the same colour.
2) In a set of horses with size n, and let f be a function on this set that produces each horse's colour. Then all horses in this set have the same colour if and only if the codomain of f on this set has size 1.
You could probably prove these are equivalent definitions.