There are several sets of numbers; each of this set are classified based on the type of numbers they hold.
The number 0 is an element of the following sets:
First, we represent the given set of number as follows:
[tex]W \to[/tex] Whole number
[tex]Z \to[/tex] Integer
[tex]N \to[/tex] Natural number
[tex]Q \to[/tex] Rational number
[tex]I \to[/tex] Irrational number
[tex]R \to[/tex] Real number
The number in each set is as follows:
[tex]W = \{0,1,2,3...\}[/tex]
[tex]Z = \{-\infty,....-3,-2,-1,0,1,2,3,....\infty\}[/tex]
[tex]N = \{1,2,3,4...\}[/tex]
[tex]Q = \{\frac{p}{q}; p,q\ E\ Z \}[/tex] --- i.e. p and q are integers
I = Non-rational numbers
[tex]R = \{W,Z,N,Q,I\}[/tex] -- all number are real numbers
Digit 0 belongs to the following sets:
[tex]W = \{0,1,2,3...\}[/tex]
[tex]Z = \{-\infty,....-3,-2,-1,0,1,2,3,....\infty\}[/tex]
[tex]Q = \{\frac{p}{q}; p,q\ E\ Z \}[/tex] ---- e.g. 0/1 = 0 means 0 is rational
[tex]R = \{W,Z,N,Q,I\}[/tex] -all number are real numbers, so 0 is real.
Base on the above analysis, we can conclude that (A), (B), (D) and (F) are correct
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