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List the numbers in set B that are natural, integers, rational, irrational amd real.
B = {-5/3, 2.060606..., 1.25, 0, 1, sqrt{5}, pi, e}
Natural: 0, 1
Integers: 0, 1
Rational: -5/3, 2.060606..., 1.25, 0, 1
Irrational: sqrt{5}, pi, e
Real: All the elements in set B are real numbers.
I think this is right.
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There is one more interesting category.
A number is called algebraic if it is the root of a polynomial equation with rational coefficients.
Non-algebraic numbers are called transcendental.
So sqrt(5) is (as you correctly say) irrational, but it is algebraic, being the root of x^2 - 5 = 0.
More complicated to prove: pi and e are not just irrational, but also transcendental.
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There is one more interesting category.
A number is called algebraic if it is the root of a polynomial equation with rational coefficients.
Non-algebraic numbers are called transcendental.
So sqrt(5) is (as you correctly say) irrational, but it is algebraic, being the root of x^2 - 5 = 0.
More complicated to prove: pi and e are not just irrational, but also transcendental.
Interesting facts. I did not know this information.
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