...Since x = y, ? (xRy ? yRx), x = y. Thus, by definition of antisymmetric, R on A is antisymmetric. Therefore, if R n R-1 ? {(a, a): a ? A}, R on A is antisymmetric. (read more)
...I was their primary caregiver throughout their childhood, and helped them with their schoolwork whenever they needed it. They both took math up through AP calculus (one of them took Calculus BC). One of them took AP Chemistry, the other took AP Physics, so I have seen some of the work done in those classes. My PhD is in Chemistry, 1988. (read more)
I am a New York State certified Mathematics Teacher (grades 7-12) and currently work as an associate consultant for Weaver Recovery Consulting, an emergency management company. I graduated with a Bachelor's degree from SUNY Oswego in 2014. I double majored in Physics (B.S.) and Mathematics (B.A.) and acquired a cumulative GPA of 3.76. (read more)
Hello! My name is Andy - I am an 11-year veteran of the U.S. Navy Submarine Force, and have since worked with both defense contractors and commercial nuclear power plants. (read more)