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Browse College Logic and Set Theory

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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]

Inverses within Semigroups [05/06/2002]

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 thing--if 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]


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.


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 Zermelo-Fraenkel (ZF) set theory.

Problem from Real Analysis [10/05/2002]

Proof by Contradiction [04/29/2003]

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 Styles--Contradiction 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?

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]

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).


Significance of Rational Numbers [01/11/2003]
Why are rational numbers defined the way they are?


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]

Truth of a Biconditional Statement [11/08/2005]

Truth of the Contrapositive [06/07/2003]


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