4 ms·
All Horses Are the Same Color
- alex-moon 3y agoThis is great. It's nice and subtle too because intuitively the theorem is true for n = 0 as well - for all the horses in the empty set, any criterion at all applies. This means if someone says "The inductive step relies on you being able to select two distinct horses, which you can't do in a set of one horse," you simply say: "Exclude horse A. Horse A is the same colour as all the horses in the remaining (empty) set. Therefore we don't need to exclude a second horse." Because that's not where the problem is.