Proof

Question 1

What are natural numbers

Answer 1

1,2,3…

Question 2

What are integers

Answer 2

Whole numbers

Question 3

how can rational numbers be represented

Answer 3

a number that can be represented as the quotient p/q of two integers such that q ≠ 0
p/q is in it’s simplest form and
both p and q cannot be even

Question 4

What are real numbers

Answer 4

Any number including irational numbers

Question 5

What letter are natural numbers represented by

Answer 5

N

Question 6

What letter are integers represented by

Answer 6

Z

Question 7

, what letter are rational numbers represented by

Answer 7

Q

Question 8

What letter are real numbers

Answer 8

R

Question 9

Disprove by counterexample

Answer 9

To disprove a conjecture all you need is to find a single instance where the injector is not true. this is called a counterexample

Question 10

Deduction

Answer 10

Direct proof, or proof by deduction is used when you need to show that a situation is true for all possible sets of numbers (when there are too many to test, i.e. infinitely many). In this case the proof consists of a set of logical steps providing a logical argument as to why the congestion must be true, and usually involves algebra (n)

Question 11

Exhaustion

Answer 11

Proof by exhaustion is used where there are a limited number of possibilities which can all be tested

Question 12

All integers can be written in three ways =

Answer 12

3k

3k-1

3k-2

because the three times table includes 3, 6
the missing numbers are a vaslue of 3 minus one and a value of three minus 2`