Proof

Question 1

Natural numbers, N

Answer 1

1, 2, 3, 4 …. etc

Question 2

Whole Numbers, W

Answer 2

0,1,2,3,4…. etc

Question 3

Integers, Z

Answer 3

…-2,-1,0,1,2…..

Question 4

Rational Numbers, Q

Answer 4

Any number that can be written as a fraction

Question 5

Real Numbers, R

Answer 5

Any numbers including e and pi

Question 6

Complex Numbers, C

Answer 6

Same as r but any n with a complex part

Question 7

Methods of proofs

Answer 7

Counter-example, Direct proof, proof by exhaustion, proof by contradiction, proof by contrapositive and proof by induction

Question 8

What can we write an even number as to make proofs easier

Answer 8

even = 2k

Question 9

What can we write as an odd number to make proofs easier

Answer 9

2k-1

Question 10

Proof by counter example

Answer 10

Often use negatives, fractions or 0 to disprove.

Question 11

Proof by exhaustion

Answer 11

Exhaust all possibilities, can also require using odds and evens

Question 12

Proof by contradiction

Answer 12

If a then b, if not b then a.
Disprove then prove true for a then b

Question 13

Proof by contrapositive

Answer 13

If a then b,
If not b then not a.
Prove

Question 14

Proving rational numbers

Answer 14

Set = to p/q