proofs

Question 1

proposition 2.3 (sqrt(2) is irrational)

Question 2

de moivre’s theorem

Question 3

the fundamental theorem of artihmetic (existence proof (prop 8.1))

Question 4

the fundamental theorem of artihmetic (uniqueness proof)

Question 5

theorem 12.1 (there are infinitely many prime numbers)

Question 6

binomial and multinomial theorems (16.2 and 16.3)

Question 7

inclusion-exclusion principle

Question 8

real numbers are uncountable

Question 9

the powerset of a set has strictly larger cardinality

Question 10

the subgroup test

Question 11

lagrange’s theorem

Question 12

differentiation formulae: power rule

Question 13

differentiation formulae: sum rule

Question 14

differentiation formulae: constant multiple rule

Question 15

differentiation formulae: product rule

Question 16

differentiation formulae: quotient rule

Question 17

→a and →b are orthogonal if and only if →a * →b = 0

Question 18

→a x →b is othogonal to both →a and →b

Question 19

general solution of the nonhomogeneous 2nd order differential equations as a sum of the complementary function and particular solution

Question 20

matrix addition (theorem 3.2)

Question 21

matrix multiplication (theorem 3.3)

Question 22

matrix transpse (theorem 3.4)

Question 23

matrix symmetry (theorem 3.5)