Recent content by hammonjj

I guess I should be slightly more specific about the work I am doing. What about the radical of a function? Could it be defined as f(x)=g(x)*g(x)? \sqrt{f(x)}

I'm currently writing a proof that relates to continuity of a bizarre function and I ran across an interesting thought, at least to me. I don't really know what a radical √ is. For example, 6^3 is: 6*6*6 and x^n is: x*x*x*x*x*x*x*x*x*x, n times, but what is a square root (ie...

I guess I'm still confused them, question C asks why you can't use this "pattern" to to find M(21), but you clearly can. It's tedious, but you just have to find all of the previous values. Thoughts?

Homework Statement So I'm taking a class that's purpose is to go over, in great detail, the concepts that secondary students learn. It's intended to prepare teachers for the material they will have to teach. Unfortunately, we are working on something called "Function Patterns" and I have...

Homework Statement Determine each of the following sets as open, closed, neither or both. a) {1/n : n \in N } b) N c) Q d) \bigcap^{∞}_{n=1}(0,1/n) e) {x: |x-5|\leq 1/2 f) {x: x^2>0} Homework Equations Open sets are sets that do not contain their boundary points. Closed sets contain...

Since x is in the interval (0,4), that is x is less than 4, (x+4)/2 is in that interval.

I think it does, but I don't know what to call it. Since my interval is a subset of the real numbers, there's some x=4-ε, where x is the maximum and ε is some tiny interval that, when subtracted from 4, gives you the maximum of the set. Am I making this too complicated? Does the max have to...

Homework Statement For each subset of ℝ, give its supremum and maximum, if they exist. Otherwise, write none. Homework Equations d) (0,4) The Attempt at a Solution For part d, if the problem were [0,4], both the supremum and maximum would be 4, since the interval includes the end...

They have one, but it's about 2 sentences long. If I'm understanding correctly: C \subseteq A So, f: C → f(C) and, therefor f^-1: f(C) → f^-1(C) I might be abusing notation a bit on this, so please correct me. What I don't understand is how exactly do I find f^-1 if it is not...

Homework Statement : Define f: ℝ→ℝ by f(x)=x^2. Find f^-1(T) for each of the following: (a) T = {9} (b) T = [4,9) (c) T = [-4,9] The attempt at a solution: So, the inverse of f should be f^-1(T)=+/-√(x). Therefor: (a) f^-1(9)= +/- 3 (b) f^-1(4)= +/- 2, f^-1(5)= +/- √(5), f^-1(6)= +/- √(6)...

In order for an equivalence relation to exist it must be symmetric, transitive and reflexive, but I don't know how to apply those.

Homework Statement Let p(x) be a polynomial in F[x]. Show that p1(x)≈p2(x) if and only if p(x)|(p1(x)-p2(x)) is an equivalence relation The Attempt at a Solution To be completely honest, I have no idea where to begin. This class has been a nightmare and this has been, by far, the worst...

Homework Statement For which values of n≥2 does the implication: axb=0 ⇔ a=0 or b=0 For some Zn (n should be a subscript) NOTE: For the a x b, the x should be the x that has a circle around it. I didn't see that symbol in the "quick symbols" :) Homework Equations I know that this...

Homework Statement Show that: 7x≈3 mod(15) Homework Equations From the given above I think it should be: 7x-3=15n The Attempt at a Solution I tried factoring this in various ways to show that either said was a factor of the other, but I'm struggling here. But I don't know...

I think it means, in order to me an Equivalence Relation, there must also exist (0,1). Correct?