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Browse College Logic and Set Theory
Stars indicate particularly interesting answers or
good places to begin browsing.
 Infinite Sets [09/24/1997]

In my algebra class we have been debating whether the integers or the
whole numbers contain more elements...
 Integer Logic Puzzle [04/22/2001]

Two integers, m and n, each between 2 and 100 inclusive, have been
chosen. The product is given to mathematician X and the sum to
mathematician Y... find the integers.
 Inverses within Semigroups [05/06/2002]

I would like to know the value of e in a semigroup for exponentiation,
if it exists. In other words what CONSTANT value e satisfies the
equation, a^b = e?
 Is There a Universal Set of All Numbers? [06/16/2004]

The real numbers and the imaginary numbers are subsets of the complex
numbers. Is the set of complex numbers a subset of a more universal
set? Is there a universal set of all numbers agreed upon today?
 Karnaugh Maps [05/07/2000]

What are Karnaugh maps? How are they used?
 Lewis Carroll's Logic Problems [01/15/1997]

Where can I find out more about Lewis Carroll's logic problems?
 Linear Topology [02/09/2003]

If a point in set X is finite, then X has a first point and a last
point. Prove by induction if true, and give a counterexample if false.
 Logical Sentences and Logical Arguments [05/16/2008]

What is the difference between A  B and A > B? They seem to mean
the same thingif A is true then you know that B is also true.
 Logic and Conditional Sentences [10/04/2005]

I am having a hard time understanding why two false statements in a
conditional sentence makes it true.
 Logic: Bayes and Popper [06/24/2003]

Is p > q totally equivalent to ~q > ~p in practice?
 Mathematical Logic [02/09/2001]

Assumptions, rules, contradictions, and a derivation.
 Math Symbols [04/07/1997]

What do the common math symbols (backward E, upsidedown A, etc.) mean?
 The Meaning of 'Or' in Logic Statements [12/19/2003]

If a logic statement says, 'James is taking fencing or algebra,' does
that mean he is taking one class or the other, or could he be taking
both of them?
 Necessary and/or Sufficient [05/26/2002]

What does it mean to say that a condition is necessary, sufficient,
or necessary and sufficient?
 Necessary and/or Sufficient Conditions with Modular Math [12/01/2006]

I'm working on a question in modular math that asks me to identify
whether given conditions are "necessary", "sufficient", or "necessary
and sufficient". I'm not sure what those terms mean.
 OnetoOne Correspondence of Infinite Sets [03/26/2001]

How can I prove that any two infinite subsets of the natural numbers can
be put in a 11 correspondence?
 Order of Quantifiers [12/19/2002]

Can you help me understand the order of quantifiers?
 Orders of Infinity [12/05/2001]

I recently read a book about infinity which set forth several arguments
for why there are different sizes or orders of infinity. None of them
seem convincing to me...
 Ordinals: Sets or Numbers? [04/16/2010]

Are ordinals sets or numbers? Doctor Tom resolves confusion around how to think
about ordinals by putting them in the context of ZermeloFraenkel (ZF) set theory.
 Problem from Real Analysis [10/05/2002]

Let X = A U B where A and B are subspaces of X. Let f:X>Y. Suppose
that the restricted functions fA:A>Y and fB:B>Y are continuous.
Show that if A and B are closed in X, then f is continuous.
 Proof by Contradiction [04/29/2003]

Is there any specific mathematical theory that states that Proof by
Contradiction is a valid proof?
 Proof of One Step Subgroup Test [05/13/2002]

Prove that a nonempty subset H of a group G is a subgroup of G if
and only if a*b^(1) is in H for all a, b in H.
 Proof StylesContradiction and Direct [04/22/2006]

Under what circumstances is it easier to prove a mathematical problem
by the method of contradiction versus direct proof? I know the
contradiction proof that sqrt(2) is irrational. Can you prove that by
direct deduction?
 Proof that 1 + 1 = 2 Using Peano's Postulates [09/12/2002]

How do I prove that 1 + 1 = 2?
 Proof that f(K) is a Subgroup of G' [11/26/2001]

If G and G' are groups, f is an isomorphism from G into G', and K is a
subgroup of G, then show that the set f(K)={f(k)\k is a member of K} is a
subgroup of G'.
 Properties of Relation [05/28/2003]

What are reflexive, symmetric, antisymmetric, and transitive
relations?
star, please
 Proving a Topology [10/11/1998]

Let X be an uncountable set of points, and T consist of the empty set and
all subsets of X whose complement is finite. Prove that T is a topology
of X.
 Russell Paradox [7/2/1996]

I'm looking for a demonstration of the Russell Paradox (there is no
ensemble of all ensembles).
 Sets N, R, C, Z, and Q [01/22/2001]

What are the exact and extensive definitions of the sets N, R, C, Z and
Q? What relation do these sets bear to one another?
 Significance of Rational Numbers [01/11/2003]

Why are rational numbers defined the way they are?
 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)?
 Subsets and Subspaces [09/07/2001]

I'm trying to extract some relations in set notation from a description
from Loomis and Sternberg's _Advanced_Calculus_...
 Sum of Uncountably Many Positive Numbers [09/15/2004]

Let S be a set of uncountably many positive numbers. I would like to
show that the sum of all the elements in S is infinite. That is,
there is no convergent sum of uncountably many positive terms.
 Transfinite Numbers [11/07/1997]

I know that Georg Cantor discovered transfinite numbers, but what are
they?
 Truth of a Biconditional Statement [11/08/2005]

Let p represent x = 0, and let q represent x + x = x. Write the
biconditional p <> q in words. Decide whether the biconditional is true.
 Truth of the Contrapositive [06/07/2003]

The inverse of a statement's converse is the statement's
contrapositive. Why?
 Understanding the Transitive, Reflexive, and Symmetric Properties [06/30/2008]

Decide if the relation 'is not equal to' is a)transitive, b)reflexive,
and c)symmetric with regard to the counting numbers.
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