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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
Is the product of two imaginary numbers always an imaginary number?
If you are talking about pure imaginary numbers (a complex number with no real part) then no. Example: bi times ci where b and c are real numbers equals b*c*i² = b*c*(-1) = -b*c, which is a real number, because b & c & -1 are all real numbers. If you're talking about multiplying two complex numbers (a + bi)*(c + di), then the product will be complex, but it could be real or imaginary, depending on the values of a, b, c, & d.
What is a definition for 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)
What is the multiplycation law of exponents?
ab x ac = ab+c, where a, b, and c are all real numbers.
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 do you prove that min of a and min of b and c equals min of min of a and b and c for all real numbers a b c where min takes two arguments?
You compare the results for each of the six possibilities: a<b<c, a<c<b, etc.
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 quotient of two real numbers with the same sign?
The sign of the quotient will be positive. +A/+B = +C. -A/-B = +C. This assumes B is not zero.
A B and C are all squared numbers. A b also a c and b c make squared numbers what are A B and c?
ab x ac = ab - ac
What is the math definition for distributive property?
a(b + c) = ab + ac where a, b and c are any 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 definition associative property multiplication?
The property states that for all real numbers a, b, and c, their product is always the same, regardless of their grouping: (a . b) . c = a . (b . c) Example: (6 . 7) . 8 = 6 . (7 . 8) The associative property also applies to complex numbers. Also, as a consequence of the associative property, (a . b) . c and a . (b . c) can both be written as a . b . c without ambiguity.
