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Browse High School Analysis
Stars indicate particularly interesting answers or
good places to begin browsing.
 Proof Involving Rational and Irrational Numbers [09/13/2004]

Prove the existence of 2 irrational numbers, a and b, where a^b is
rational.
 Proofs of e [03/21/2002]

I found out that the definition of e is: e = lim, as n approaches
infinity (1+1/n)^n. Is there a proof for this or for 1+2(e1/n)?
 Prove S' Closed in R^n [10/07/2002]

Prove that S' (the derived set or set of all accumulation points of S)
is closed in R^n.
 Prove That a Set Is Uncountably Infinite [10/31/1997]

Prove that the set [0,1]x[0,1] is uncountably infinite.
 Prove the Commutative Law [4/1/1996]

I have a question that may sound very silly: can anyone PROVE the
commutative law?
 Proving a Set is Closed [04/15/1998]

Let f be a continuous real valued function on Rn, and let S = {x in Rn :
f(x) = 1}. Prove that S is a closed subset of Rn.
 Proving/Deriving the Quadratic Equation [4/1/1996]

How can one derive the quadratic equation, i.e. prove it?
 Proving Limits at Infinity Using the Formal Definition [04/11/2004]

We are required to find a limit (informally), then prove that our answer is correct by using the formal definition of limits. I'm not sure I'm on the right track.
 Proving Limits Formally [01/04/1999]

Given a sequence, I can guess what the limit it. How do I actually prove
my guess is the limit?
 Proving the Properties of Natural Numbers [03/08/2000]

How can you prove or derive the commutative, associative, and
distributive properties of numbers?
 Rational/Irrational Numbers [03/12/1999]

Prove that between any two numbers there are a rational and an irrational
number and, therefore, that there are infinite numbers of each.
 Real Analysis [9/13/1996]

Let I be a subset of R where I is an interval and let f map I to R be
increasing on I...
 Real Plane, Complex Plane [09/16/2002]

When does Az + Bz + c = 0 become a straight line?
 Set Notation via Broken Typewriter [11/19/2002]

I have a machine that only types out ones (no spaces or tricks
involved). What procedure must you do to this machine to get any given
finite set? For example [2,85,11,5,60]. For a different set, the
number of ones that the machine types out will vary.
 Significant Difference? [05/08/1999]

A research question: does mean delivery time differ for boy babies and
girl babies?
 Singularity [03/01/1999]

What is a singularity?
 Sizes of Infinities [01/31/1997]

How can you prove that one infinity is larger than another?
 Solving the Equation x^y = y^x [12/09/2004]

Solve x^y = y^x for x in terms of y only. Also, how do I find all
possible solutions beyond the obvious ones of x = y, (2,4), and (4,2)?
 A Sorting Lower Bound [10/01/1998]

Show that you cannot sort 3 elements with 2 comparisons, an example of
lower bound.
 Sum of Convergent Series [09/25/1999]

How can you find the sum for k = 0 to infinity of 1/[(k+1)(k+3)], and the
sum for k = 0 to infinity of [(25/10^k)  (6/100^k)]?
 Teaching Synthetic Division [10/23/1996]

Do you have any advice for teaching synthetic division, on the computer,
to the rest of my class?
 Two Definitions of Limits, with Examples [05/11/1998]

Epsilondelta definitions of the limit of a function and the limit of a
sequence.
 An Uncountable Set [09/28/1998]

How do you prove, using diagonalization, that the set of functions from N
to N is uncountable?
 Using L'Hopital's Rule [01/22/1999]

Prove that e^(1/3) is the limit for y =(arctan(x)/x)^(1/(x^2)) when x >
0.
 Using Newton's Method to Solve an Implicit Equation [10/14/2007]

How can I solve the equation (sin(X))/X = 0.7031? My book gives the
answer but does not explain how to find it.
 Weierstrass Curve [09/13/2002]

About 100 years ago the mathematician Weierstrass gave an example of a
curve consisting of angles, or corners, and nothing else. Where can I
find this equation?
 What is 0.999... + 0.999...? [09/27/1999]

How can I show that 0.999... + 0.999... = 2?
 What is 1^infinity? [12/10/1998]

Why is 1^infinity indeterminate? How can you show this using limits? Why
is it not equal to 1, as intuition leads us to believe?
 X^Y = Y^X [11/13/2002]

Find (with proof) all pairs of integers {x,y} that satisfy x^y=y^x.
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