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Question 1

natural numbers

Answer 1

natural numbers we mean the elements of the set N := {0,1,2,…}.

Question 2

integers

Answer 2

integers are the elements of the set Z := {…,−2,−1,0,1,…}.

Question 3

rational numbers

Answer 3

denoted Q the fraction field of Z

Question 4

real numbers

Answer 4

R

Question 5

c complex numbers

Answer 5

I = square root of -1 to R

Question 6

INDUCTION PRINCIPLES

Answer 6

1) if P(0) is true P(n) implies P(n+1) then P(n) is true for all n in N
2)if P(k) true for all k<n implies P(n), then P(n) is true for all n in n
3) Every non-empty subset A of N has a minimum