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Cantor, Peano, Natural Numbers, and Infinity [03/19/1998]

A conversation on transfinite numbers and contradictions the questioner believes exist in Cantor's paper introducing the diagonal method.

Cardinal and Ordinal Numbers [01/08/1997]

How can 3 be both a cardinal and ordinal number at the same time?

Defining Kinds of Numbers [03/21/1997]

Could you please define: perfect numbers, deficient numbers, square numbers, abundant numbers, amicable numbers, and triangular numbers?

Diagram for Math Numbers [10/05/1997]

My daughter is doing a tree diagram using terms related to math "numbers." Could you please explain in lay terms what surds are?

Difference Between Zero and Nothing [12/12/1996]

What is the difference between zero and nothing?

Infinite Sets [07/17/1997]

How do you prove that there are more rational numbers than negative integers? How can you tell if an infinite set is countable or uncountable?

Intersection, Difference, Union [12/18/2002]

Please explain: integers that are members of A but not of B, integers that are members of both A and B, and integers that are members of either A or B?

Intersection of Sets [10/02/2000]

I do not understand intersection of sets. Can you give me an example?

Line Segments and Size of Infinites [03/19/1997]

Divide a line segment into three parts, one half and one a quarter the length of the line segment. Choose a point at random along this line segment. What is that probability that this point lands in the 1/2 segment...?

Lines, Points, and Infinities [09/01/2001]

What is the cardinality of the set of real numbers between 0 and 1? Is this cardinality less than, greater than, or equal to the cardinality of real numbers between 0 and 2?

One-to-One Correspondence and Transfinite Numbers [12/10/1999]

Can you explain what Cantor meant by one-to-one correspondence, and transfinite numbers?

Rational and Irrational Numbers [11/12/1997]

Which set is bigger, the set of rational or irrational numbers?

Rational Numbers [11/24/1997]

Which is greater, the number of rational numbers between 0 and 1 or the number of rational numbers between 0 and 2?

Sets and Subsets [1/23/1995]

My teacher said that integers are a subset of reals, and whole numbers are a subset of integers, and counting numbers are a subset of whole numbers, and so on and so forth. What does that mean?

Set, Subset, Element [3/10/1997]

Please define: set, subset, member, element, intersection, union.

Sets: Unions and Intersections [12/17/1997]

I want to know about complements, union, intersection, and sets of numbers.

Set Theory and Orders of infinity [04/08/1997]

Given a lists of sets, such as all real numbers between 0 and 1, the integers, the odd integers, etc. how do I compare their size? And what does this have to do with Cantor's set theory?

Unions and Intersections [2/9/1995]

In my text, there are these upside-down horseshoe looking things, and there is no explanation of what they are or why they exist...

What are Sets and Subsets? [09/06/2001]

Can you please give me examples of sets and subsets?

What is a Set? [04/04/1997]

What is the correct term to refer to groups of objects like 3 cars, 7 pencils, or 5 apples?

Abundant and Deficient Numbers [10/14/1997]

What are abundant and deficient numbers, and what are they used for?

Aleph Null [01/22/1998]

What does aleph null represent?

Are They Wearing Seatbelts? [3/26/1995]

80 percent of all California drivers wear seatbelts. If 4 drivers are pulled over, what is the probability that all 4 will be wearing their seatbelts?

Bijections [04/28/2003]

Find a bijection from (0, 1) to (0, 1]. (Be sure to prove that your function has the proper properties.)

Borel fields [08/10/1997]

From the definition given in my book for an algebra, I don't understand why EVERY algebra would not be a Borel field.

Bounded Set [06/24/2003]

Let S be a set of real numbers. Prove that the following are equivalent: (a) S is bounded, i.e. there exists a number M greater than 0 such that abs(x) is less than or equal to M for every x in S; (b) S has an upper bound and lower bound.

Building Sets [05/26/2002]

Is 5 part of the set {x:x is a multiple of 7 and 5 < x < 56}?

Cardinality between Open and Closed Sets [09/20/2001]

I would like to know how to prove that the sets (0,1) and [0,1] have the same cardinality.

Closed Set of Elements [06/30/2001]

Please explain the term 'closed' in the following sentence: '...the set of complex numbers is CLOSED under addition...'.

Closed Sets [02/27/1999]

Is a union of finite number of closed sets and the intersection of any number of closed sets closed?

Closure and Compactness in a Metric Space [10/08/2002]

Regard Q, the set of all rational numbers, as a metric space, with d(p,q)=|p-q|... Show that E is closed and bounded in Q, but that E is not compact. Is E open in Q?

Closure and the Reals [03/26/1998]

Under what set of operations are the positive real integers closed?

Closure Property [12/22/1998]

Simple definition and examples of closure property.

Compact Sets and Hausdorff Spaces [03/19/2003]

How do you prove that every compact subset of a metric space is closed?

Complement of a Set [08/14/2003]

What is a universal set?

Complements, Unions, and Intersections of Sets [10/13/2004]

A visual example of how to shade in the complement, union, and intersection of sets in a Venn diagram.

Connected Sets in Topology [04/22/1998]

Exploring connected sets with examples in Euclidean space.

Countability of Primes and Composites [05/18/2002]

If the union of two sets is countable, can either of the sets be uncountable?

Countable Sets and Measure Zero [05/12/2001]

How would you prove that if a set S is countable, then S has measure zero?

Definition of Equal and Equivalent Sets [05/31/2004]

Write a set that is equivalent to, but not equal to, the set (a, b, c, d, e, f). Would the answer be all the same letters, just arranged in a different order?

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