Try solving this answer from my son's math test?

Question

If we replace normal multiplication of real numbers with an operation between two real numbers defind as follows a*b=2a+b. Is the set of real numbers, R, a field using normal addition, and using this * operation in place of the usual multiplication? Please prove answer.

my son is in high school

Answer 1

Okay here. I think this solves it.

Proof:

1. a*b = 2a+b ~ Given
2. a 3. a+a < b+a ~ Adding "a" to both sides of inequality
4. 2a 5. 2a+b< b+b+a ~ adding "b" to both sides, b*a = 2a+a
6. 2a+b<2b+a ~ Since a*b = 2a+b
7. a*b 8. therefore, a*b 9. therefore, R is not a field

lol that took a long time. My eyes r like -_- must rest my head. Okay i hope taht helps =D if it doesnt then....=(...just say i dont noe and ask the teacher or something o.O

-joe coool

Answer 2

Great answer above, but no way is that ordinary high school math. It is not even ordinary college math. Maybe graduate work for math majors.

"In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers."

Abstract algebra? In high school?

Answer 3

uhhhh, try this.

AB=A*B=A x B= A times B.

A*B is not = 2A + B.

2A+B = ( 2 * A) + B = (2 x A) + B.

I didn't understand your question because you are illiterate, but I hope this helps a little at least.

Answer 4

It might work if a=(-1) b=1.

Answer 5

What grade is your son in????

Abstract Algebra is a college level discipline.

Answer 6

What the heck was the question?

Answer 7

liver doesnt tast good eat steak..