Euro S. 1st year - Jacques Ruffié
Test on NUMBERS and SETS : correction
I- A prime number is a natural number which has exactly two distinct divisors: 1 and itself (the word ”distinct”
is essential because 1 is not a prime number); 61, 67 and 71 are three prime numbers greater than 60.
II- Two natural numbers are coprime if and only if their GCD is 1. This can be proved with the Euclidean
algorithm, the repeated subtractions or simply with the list of factors (the development of one of these
methods was expected).
III- The expression ”S ⊂ E” is read ”S is a subset of E” or ”S is included in E”; it means that every element of
S is an element of E.
IV- a) π ∈
/ Q, the number π is not a rational number;
b) N ⊂ R, every natural number is a real number;
√
c)
2 ∈ R, the square root of two is a real number;
d) N ⊂ Z, every natural number is an integer (or a relative integer).
Euro S. 1st year - Jacques Ruffié
Test on NUMBERS and SETS : correction
I- A prime number is a natural number which has exactly two distinct divisors: 1 and itself (the word ”distinct”
is essential because 1 is not a prime number); 61, 67 and 71 are three prime numbers greater than 60.
II- Two natural numbers are coprime if and only if their GCD is 1. This can be proved with the Euclidean
algorithm, the repeated subtractions or simply with the list of factors (the development of one of these
methods was expected).
III- The expression ”S ⊂ E” is read ”S is a subset of E” or ”S is included in E”; it means that every element of
S is an element of E.
IV- a) π ∈
/ Q, the number π is not a rational number;
b) N ⊂ R, every natural number is a real number;
√
c)
2 ∈ R, the square root of two is a real number;
d) N ⊂ Z, every natural number is an integer (or a relative integer).
Euro S. 1st year - Jacques Ruffié
Test on NUMBERS and SETS : correction
I- A prime number is a natural number which has exactly two distinct divisors: 1 and itself (the word ”distinct”
is essential because 1 is not a prime number); 61, 67 and 71 are three prime numbers greater than 60.
II- Two natural numbers are coprime if and only if their GCD is 1. This can be proved with the Euclidean
algorithm, the repeated subtractions or simply with the list of factors (the development of one of these
methods was expected).
III- The expression ”S ⊂ E” is read ”S is a subset of E” or ”S is included in E”; it means that every element of
S is an element of E.
IV- a) π ∈
/ Q, the number π is not a rational number;
b) N ⊂ R, every natural number is a real number;
√
c)
2 ∈ R, the square root of two is a real number;
d) N ⊂ Z, every natural number is an integer (or a relative integer).
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