I had a great right up for you, but when I posted it I was timed out and had to login in (drives me nuts!) and lost everything. I don't have time to write it again, but here is a short version.
g'(x) is
+ (-inf, -8.8)
- (-8.8, -8)
- (-8, -7.2) Asymptote at -8
+ (-7.2, + inf)
I...
Could you just draw a (x,y) and (u,v) circles and show their radii and origins are identical and say its obviously reflexive, symmetric, and transitive?
They both lie on a circle. I can prove they're equal through distance formula at any given point of origin.
How do you geometrically interpret reflexivity, symmetry, and transitivity? I mean, it's obvious to me visually, but how do you prove it?
Story of my life: "It's obvious...
That makes sense conceptually, but I'm not quite sure how to apply it. If we're letting x2+y2 equal to diameter one, what happens to our (u, v)? I'm confused how to get this to work. What do we define the relation as?
Homework Statement
For (x, y) and U, v) in R2, define (x,y)~(u,v) if x2+y2 = u2+v2. Prove that ~ defines an equivalence relation on R2 and interpret the equivalence classes geometrically.
Homework Equations
(none)
The Attempt at a Solution
The first part is easy. I proved...
I've been having trouble partitioning number systems into sets. The complex and rational number systems blow me away, so I'll stick with all reals, integers, and naturals for now.
Homework Statement
1a) With five sets of infinitely many positive integers, partition the set of all real...