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Selected answers to common questions:
- Sets, Injection, and Surjections [12/04/1998]
If S is a set, such that every injection A from S to S is also a
surjection, does S have the property that every surjection A from S to S
is also an injection?
- 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?
- Stirling Numbers [05/26/1999]
Can you show how to evaluate Stirling Numbers of the first and second
- Subsets and Greatest Common Divisor [03/26/1999]
A question on subsets and another on greatest common divisor (GCD).
- Subsets and Proper Subsets [07/10/1998]
What is the difference between a subset and a proper subset?
- Subsets of Real Numbers and Infinity [08/22/2001]
Am I correct in saying that both the whole number set and the integer set
have an infinite number of numbers within them, and therefore are of the
- Sum of Integers in a Set [06/19/2001]
Consider the set of all four-digit integers, each of which is formed
using the digits 1,2,3,5, or 7 at most once. Find the sum of the integers
in this set.
- Sum of Set Numbers [07/02/2001]
a_1, a_2, a_3,....a_15 are positive real numbers... what is the smallest
possible value of the largest of a_1, a_2, a_3...a_15?
- Total Membership [08/20/1999]
At a country club 35 people play golf, 28 swim, and 24 play tennis. Of
these, 6 play golf and tennis only, 9 play golf and swim only, and 7 play
tennis and swim only. 8 people do all three. How many members are there
- Transfinite Arithmetic [10/28/1997]
What is transfinite arithmetic? I pretty much know what it means, but I
am having trouble applying it to aleph-null.
- Transfinite Numbers [11/07/1997]
I know that Georg Cantor discovered transfinite numbers, but what are
- Truth Table [04/14/1999]
Prove that the complement of X intersects Y = X' union Y' without using a
- Types of Numbers [10/30/1998]
How are the different types of numbers related? For example, what about
counting, whole, rational, irrational, integers, prime, ... ?
- Union and Intersection of Empty Family of Sets [03/20/2003]
In what sensible way can we define the union and intersection of an
empty family of sets?
- Unions and Intersections [05/10/1999]
How are the union and intersection of sets related?
- Unions and Intersections: Proving Sets [10/17/1999]
How can I verify a proof of the statement A - (B union C) = (A - B)
intersect (A - C)?
- Universal Sets [08/19/2002]
If I had to place the President of the U.S. in three universal sets,
what are some possibilities?
- Unknown Numbers and a Venn Diagram [11/26/2001]
The GCF of two numbers is 20 and the LCM is 840. One of the numbers is
120. Explain how to find the other number and use the Venn diagram method
- Venn Diagram - Choose One of Three Options [01/24/1999]
Members of a computer class choose at least one of three options. How
many are taking just one? ... Use a Venn diagram.
- Venn Diagram: Goops, Gorps, Gorgs [09/19/2002]
Every Goop is a Gorp. Half of all Gorgs are Gorps. Half of all Gorps
are Goops. There are 40 Gorgs and 30 Goops. No Gorg is a Goop. How
many Gorps are neither Goops nor Gorgs?
- Venn Diagram of Natural Numbers [09/22/1999]
How can I construct a Venn diagram comparing the numbers 1 through 100 in
these 4 areas: odd, even, composite and prime?
- Venn Diagram of Our Number System [12/13/2002]
I don't know how to include complex numbers that consist of a real
part and an imaginary part. Can you please diagram this for me?
- Venn Diagram to Classify Quadrilaterals [01/02/2003]
I am looking for a Venn diagram that will accurately display the
relation among trapezoids, parallelograms, kites, rhombi, rectangles,
- What is a Loop? [10/06/1997]
Further, exactly what is _an_ algebra? Thirdly, what is a Lie group?
- What is a Subset? [10/13/2001]
I would like to know what a subset is.
- What is a Venn Diagram? [02/26/1998]
What is a Venn Diagram? What is its use, definition, and what does it
- Z Values in the Mandelbrot Set [04/27/2006]
Could you please explain why for the Mandelbrot set the modulus for
the resulting z value must remain less than 2?