**Theorem:** Every positive integer is interesting.**Proof:** By contradiction, assume that there exists an uninteresting positive integer. Then there must be a smallest uninteresting positive integer. But that's pretty interesting! Therefore a contradiction!

(I really doubt that you will manage to proof this one in school..)

Top ten excuses for not doing homework:

1. I accidentally divided by zero and my paper burst into flames.

2. It was Isaac Newton's birthday.

3. I could only get arbitrarily close to my textbook. I couldn't actually reach it.

4. I have the proof, but there isn't room to write it in this margin.

5. I was watching the World Series and got tied up trying to prove that it converged.

6. I have a solar powered calculator and it was cloudy.

7. I locked the paper in my trunk but a four-dimensional dog got in and ate it.

8. I couldn't figure out whether I am the square root of negative one or i is the square root of negative one.

9. I took time out to snack on a doughnut and a cup of coffee. I spent the rest of the night trying to figure which one to drink.

10. I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it**Q:** What is the world's longest song? **A:** "Aleph-nought Bottles of Beer on the Wall."

(Aleght-nought is infinity. It is from Group theory)

A story:

Some famous mathematician was to give a keynote speech at a conference. When he was asked for an advance summary, he said he would present a proof of Fermat's Last Theorem -- but they shouldn't announce it. Although when he arrived, he spoke on a much more prosaic topic. Afterwards the conference organizers asked why he said he'd talk about the theorem and then didn't. He replied that this was his standard practice, just in case he was killed on the way to the conference.

Another story:

I don't know if the previous story was real but this one is:

WHEN G. H. Hardy faced a stormy sea passage from Scandinavia to England, he took out an unusual insurance policy. Hardy scribbled a postcard to a friend with the words: "Have proved the Riemann hypothesis". God, Hardy reasoned, would not let him die in a shipwreck, because he would then be feted for solving the most famous problem in mathematics. He survived the trip.

Lottery:

A mathematician organizes a lottery in which the prize is an infinite amount of money. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment:

"1 dollar now, 1/2 dollar next week, 1/3 dollar the week after that..."

(This is a reason for not playing with mathematician in math games. Also as a interesting fact, you chance of winning in a real world lottery is less then the possibility that you will die this week.)

Entropy Modulo a Prime (Continued)

2 days ago

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