Mathematical Paradox

Hello World

The responses that I got on my previous posts were quite good. A lot of people were fascinated by the time travelling paradoxes so I decided to write about the paradoxes in mathematics too. Well my posts on a particular topic will now come occasionally but don't forget to check The Branched Timeline Scientific Dictionary as 10 new words with their meanings will be posted there everyday so you can enhance your scientific vocabulary by reading it. 

A mathematical paradox is a mathematical conclusion so unexpected that it is difficult to accept even though every step in the reasoning is valid. 

There are lots and lots of paradox so I'll try to get as many mathematical paradoxes as possible. If any paradox is missed it will be updated in future.

1. Pythagorean Paradox/Staircase Paradox

Is Pythagoras Theorem always true? Is 3+4=5 ? 

2. Zeno Paradox

3. Russel & Barber Paradox

4. Infinite Hotel Paradox

How a hotel having infinite rooms ran out of rooms.

5. Aristotle Wheel Paradox

Circumference of small circle and big circle equal ?

6. Gabriel Horn Paradox

7. Ramanujan Paradox

Sum of natural numbers negative ?

8. Toroflux Paradox

How N+1=N ?

9. Riemann's Paradox

How infinity subtracted from infinity can give pi ?

10. Godel's Incompleteness Theorem

I am a liar. Is this statement true or its a lie?

11. Apu's Paradox

Sum of positive numbers 0 ?

Question

What is your favourite paradox ?