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For all real numbers a b and c?
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Show that the set of all real numbers is a group with respect to addition?
Closure: The sum of two real numbers is always a real number. Associativity: If a,b ,c are real numbers, then (a+b)+c = a+(b+c) Identity: 0 is the identity element since 0+a=a and a+0=a for any real number a. Inverse: Every real number (a) has an additive inverse (-a) since a + (-a) = 0 Those are the four requirements for a group.
What is the name for all sets of numbers?
There is a hierarchy of sets:Counting numbersNatural numbers (N)Integers (Z)Rational numbers (Q)Real numbers (R)Complex numbers (C)Quaternions, and possibly more.
How to evaluate 2a plus 6b?
2a + 6b = c, where a, b, and c are all numbers from the domain of your choice. Usually, in algebra, the real number set R is used as the domain. In this case, you would need to select values from R for a and b which will yield the value of c. Since this function is closed in the real number system, c will always be a real number, given that a and b are real numbers.
What is the sum of complex numbers?
In (a+bi) + (c+di), you add the real parts using the laws for real numbers and do the same for the imanginary parts. (a+c)+(b+d)i
