Theorems Jokes

A Calculus Carol
written by: Denis Gannon (1940-1991)
sung to the tune of "Oh, Christmas Tree"
Oh, Calculus; Oh, Calculus,
How tough are both your branches.
Oh, Calculus; Oh, Calculus,
To pass what are my chances?
Derivatives I cannot take,
At integrals my fingers shake.
Oh, Calculus; Oh, Calculus,
How tough are both your branches.
Oh, Calculus; Oh, Calculus,
Your theorems I can't master.
Oh, Calculus; Oh, Calculus,
My Proofs are a disaster.
You pull a trick out of the air,
Or find a reason, God knows where.
Oh, Calculus; Oh, Calculus,
Your theorems I can't master.
Oh, Calculus; Oh, Calculus,
Your problems do distress me.
Oh, Calculus; Oh, Calculus,
Related rates depress me.
I walk toward lampposts in my sleep,
And running water makes me weep.
Oh, Calculus; Oh, Calculus,
Your problems do distress me.
Oh, Calculus; Oh, Calculus,
My limit I am reaching.
Oh, more...

A Calculus Carol
written by: Denis Gannon (1940-1991)
sung to the tune of "Oh, Christmas Tree" Oh, Calculus; Oh, Calculus,
How tough are both your branches.
Oh, Calculus; Oh, Calculus,
To pass what are my chances?
Derivatives I cannot take,
At integrals my fingers shake.
Oh, Calculus; Oh, Calculus,
How tough are both your branches.
Oh, Calculus; Oh, Calculus,
Your theorems I can't master.
Oh, Calculus; Oh, Calculus,
My Proofs are a disaster.
You pull a trick out of the air,
Or find a reason, God knows where.
Oh, Calculus; Oh, Calculus,
Your theorems I can't master.
Oh, Calculus; Oh, Calculus,
Your problems do distress me.
Oh, Calculus; Oh, Calculus,
Related rates depress me.
I walk toward lampposts in my sleep,
And running water makes me weep.
Oh, Calculus; Oh, Calculus,
Your problems do distress me.
Oh, Calculus; Oh, Calculus,
My limit I am more...

For all those serious Maths buffs... lemmas and theorems!
1. Lemma: All horses are of the same colour.
Proof (by induction):
Case n=1: In a set with only one horse, it is obvious that all horses in that set are the same colour.
Case n=k: Suppose you have a set of k+1 horses. Pull one of these horses out of the set, so that you have k horses. Suppose that all of these horses are the same colour. Now put back the horse that you took out, and pull out a different one. Suppose that all of the k horses now in the set are the same colour. Then the set of k+1 horses are all the same colour. We have k true => k+1 true; therefore all horses are of the same color.
2. Theorem: All horses have an infinite number of legs.
Proof (by intimidation):
Everyone would agree that all horses have an even number of legs. It is also well-known that horses have forelegs in front and two legs in back. 4 + 2 = 6 legs, which is certainly an odd number of legs for a horse to have! Now more...