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Why are irrational numbers called surds?
Irrational number are NOT called surds. For example, pi is irrational but it is not a surd.Surds are a very small subset of irrational numbers.
Which of these sets of numbers is not a subset of the real numbers irrational integer rational and imaginary?
Imaginary numbers are not a subset of the real numbers; imaginary means not real.
What is the relation between integers natural numbers whole numbers rational and irrational numbers?
Natural numbers = Whole numbers are a subset of integers (not intrgers!) which are a subset of rational numbers. Rational numbers and irrational number, together, comprise real numbers.
What is the intersection of the rational numbers and the irrational numbers?
Some would say that there is no intersection. However, if the set of irrational numbers is considered as a group then closure requires rationals to be a proper subset of the irrationals.
Why isn't an irrational number included in the Venn diagram of Families of numbers?
An irrational number is included in the Venn diagram of real numbers. The subsets of the set of the real numbers are: The set of all natural numbers, N; the set of all whole numbers, W; the set of all integers, I; the set of all rational numbers, Q; and the set of all irrational numbers, S. It is obvious that N is a subset of W, W is a subset of I, and I is a subset of Q, but similar relationship doesn't hold between Q and S. However, this fact does not mean that irrational numbers are not in the Venn diagram, because they are also real numbers as well.
