mathametical reasoning

1. Prove that is an irrational number by contradiction method.

2. Pinocchio has a nose, which is growing when is lying. Pinocchio says, “My nose is growing”. Is he lying or telling the truth?

3. A) Draw a complex number coordinate space

B) Show a complex number in this space, name it C

C) Show the magnitude of C geometrically

D) Calculate the magnitude of C

E) Calculate the square of C, name it as C2, show it on the space

F) Calculate the magnitude of C2

4. What are the four points of Hilbert’s Plan? (Formal Axiomatic System)

5. What did Hilbert proposed, and how did Gödel disprove him?

6. Think of Platonic Mathematics and what Plato proposed. And now explain who is closer to Plato? Hilbert or Gödel? Why?

7. Gödel proved that a closed mathematical system cannot be validated with in the system itself in his second theory. So apply this claim to physics and cosmos.

8. “Mathematical Word is a discovery”. Who can claim this? Hilbert or Gödel? Why?

9. After the mathematisation of cosmos by Newton, scientists started to believe that cosmos is as logical as mathematics. Everything in cosmos was behaving according to some mathematical formulas, however we were completely wrong to think the cosmos as logical. Why?

10. Write the steps of inductive proof. And apply this proof method to the Gauss summation formula.