I don't remember where I heard this, but I still like it a lot.
Proof Techniques #2: Proof by Oddity
Sample: To prove that horses have an infinite number of legs.
I went out and counted my horse's legs and my my daughter's horse's legs, and all I could find was 4 on each of them. Are they deformed? Yikes!!
I like this one better:
All horses are the same color.
Proof:
We proceed by induction.
Base case:
There is only one horse, and it is the same color as itself, so therefore the assertion is true for this case.
Inductive step:
Suppose that whenever we have n horses, they are all the same color. Now suppose we have n+1 horses. If we remove one horse, by our hypothesis, all the remaining horses have the same color. If we remove a different horse, all the remaining horses also have the same color, and this collection includes the original horse we removed. Thus all n+1 horses have the same color.
We conclude any number of horses all have the same color.
You people are wrecking my mind.
I’ve never heard the idea that infinity is both odd & even, but your post is entertaining none the less.
hypothosis 2 is not a correct interpretation of English, thus rendering the rest of the arguments invalid
I could not resist sharing this on Facebook.