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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.
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 definition associative property of addition?
The property which states that for all real numbers a, b, and c, their sum is always the same, regardless of their grouping:(a + b) + c = a + (b + c)
How do you work out what bc is in algbra?
Algebraic Properties of Real Numbers The basic algebraic properties of real numbers a,b and c are: Closure: a + b and ab are real numbers Commutative: a + b = b + a, ab = ba Associative: (a+b) + c = a + (b+c), (ab)c = a(bc) Distributive: (a+b)c = ac+bc Identity: a+0 = 0+a = a Inverse: a + (-a) = 0, a(1/a) = 1 Cancelation: If a+x=a+y, then x=y Zero-factor: a0 = 0a = 0 Negation: -(-a) = a, (-a)b= a(-b) = -(ab), (-a)(-b) = ab
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
