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Is 0 imaginary?
0 is a real number because it is part of the whole, integer, and rational number family which is in the section under real numbers (not imaginary).
Do real numbers have a multiplicative inverse?
All real numbers, except 0, have a multiplicative inverse. For any real x, (x not = 0), there exists a real number y such that x*y = 1. This y is denoted by 1/x.
Show that the set of all real numbers is an abelian group with respect to addition?
Sure thing, honey. The set of all real numbers is indeed an abelian group under addition. It's closed because adding two real numbers gives you another real number. It's associative because math plays nice like that. The identity element is 0, and every real number has an inverse (just slap a negative sign in front of it). Plus, addition is commutative, so you can add those numbers in any order and still get the same result. Voilà, you've got yourself an abelian group!
Is every real number a complex number?
A complex number is a number of the form a + bi, where a and b are real numbers and i is the principal square root of -1. In the special case where b=0, a+0i=a. Hence every real number is also a complex number. And in the special case where a=0, we call those numbers pure imaginary numbers. Note that 0=0+0i, therefore 0 is both a real number and a pure imaginary number. Do not confuse the complex numbers with the pure imaginary numbers. Every real number is a complex number and every pure imaginary number is a complex number also.
All whole numbers greater than 0 are also called the integers?
All whole numbers greater than 0 are also called the __:)__________ integers. positive
