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	Some questions about sets		2019-12-15
		M.Azzi pose la question : Hello, (I) - In set theory can a given set contain both elements and subsets, as "elements", as in : A = {1,2,{},3,{{3}},8} If yes : 1 - then, is |A| = 6 ? 2 - if the empty set is a subset of every set, 2. 1. does {} = {{}}, {{{}}} etc? , and if the is true what are the respective cardinals of the latter three? (0,1,1?). 2 . 2. Why isn't {1} equal to {{},1}? and why should these two be equal without having the same cardinality? Sorry if my questions are not well expressed. Thank you for the great service you provide. Harley Weston lui répond.
	Combinations of cities		2019-12-03
		Oliver pose la question : Hi! I'm looking to find out how many combinations (non repeating) there are for 6 cities. If we name the cities A to F, possible combinations would include; A. A, B. B. A, B, C. A, C. B, C. C. and so on. Thank you! Penny Nom lui répond.
	nC0 + nC1 + nC2 + .... + nCn = 2^n		2018-02-19
		bristal pose la question : (QQ) Prove, nC0 + nC1 + nC2 + .... + nCn = 2^n. Penny Nom lui répond.
	Subsets		2016-06-26
		Kats pose la question : How Many sub sets are in set k={6,7,3} Penny Nom lui répond.
	Countable and uncountable sets?		2016-01-15
		wilson pose la question : what are the countable and uncountable sets? Penny Nom lui répond.
	The number of possible musical notes using an n-key instrument		2015-05-04
		Farihin pose la question : Lets say that i have keys, and each key is for notes of a musical instrument, So i wanted to find out the number of notes i can get for a certain number keys, of course in the form of an equation. Notes can use as many keys, it can use 1, or 2, or 3, or even 100. Notes in real life is not as such, but ignore reality. I tried doing this but i can't seem to find a formula for it. For example, i have 4 keys, say A, B, C, and D. so, for notes that uses one key are 4, which is A, B, C, and D themselves. for notes that uses two keys are 6, AB, AC, AD, BC, BD and CD. for notes that uses three keys are 4, ABC, ABD, ACD and BCD. lastly for notes that uses all four keys is 1, ABCD. So, the total will be 4+6+4+1=15# The nth term for the first equation is n, the second is [(n^2)-n]/2 the third and the fourth, i don't know but the final answer should be like, n + [(n^2)-n]/2 + [3rd] + [4th] Sorry for the long question though... Penny Nom lui répond.
	A question in set theory		2015-02-25
		Jared pose la question : If a set A={1,2,3} and set B={ {}, 1} Can B be a subset of A? Since every Set contains an {} ? Robert Dawson and Claude Tardif lui répond.
	Overlapping sets		2014-05-23
		daniel pose la question : motors inc manufactured 325 cars with automatic transmission,216 with power steering ,and 89 with both these options. How cars were manufactured if every car has at least one option? Penny Nom lui répond.
	Equivalent sets		2012-09-13
		asif pose la question : show that (-1,1)~(1,1) or give its counter example Harley Weston lui répond.
	The power set of A		2012-03-24
		rashdin pose la question : Can you find a set A, |A|=4 and define a bijective function between A and P(A)? Penny Nom lui répond.
	Properties of real numbers applied to subsets		2012-02-01
		Mark pose la question : Hello - The questions that I have for you is do the properties of real numbers (such as the associative, commutative, identity, inverse, and distributive law) apply to ALL the subsets of real numbers? In other words, do all those properties work for the Natural Numbers? The Whole Numbers? And so on and so forth. I understand that they are all real numbers, but for instance: the identity is whenever you add zero to a number, you get that number back. But does that work with, say, with only the odd numbers? Zero isn't odd so can that property actually apply to JUST the odd numbers? Any consideration would be greatly appreciated! Robert Dawson lui répond.
	Cardinality of infinite sets		2009-09-01
		Brian pose la question : I was reading an answer to a question on your site regarding infinite sets (http://mathcentral.uregina.ca/QQ/database/QQ.09.01/carlos1.html), and I think they may have got the answer wrong. I his example, he claims that the set of real numbers BETWEEN 0 AND 1 is larger than the set of positive integers. Please correct me if I am wrong, but I believe those two sets are -- pardon the expression -- equally infinite. For any integer, there is a corresponding real number between 0 and 1, and vice versa. For instance, using the decimal as a "mirror", you can create a mirror image of any real number between 0 and 1 as an integer (i.e. 0.1234 gets mirrored as the integer 4321 -- I could write it out algebraically, if you want, but you get my point) Am I wrong? Thanks, Brian Victoria West lui répond.
	Subsets		2009-06-16
		Tracy pose la question : Suppose C is the subset of D and D is the subset of C. If n(c)=5, find n(D) What other relationship exists between sets C and D? Penny Nom lui répond.
	The axiom of choice and constructibe sets		2009-04-10
		sydney pose la question : The axiom of choice asserts the existence of certain sets, but does not construct the set. What does "construct" mean here? For example, does it require showing the existence and uniqueness of some function yielding the set? In general, what does it mean to require the existence of a mathematical object be tied to a construction of it? Claude Tardif lui répond.
	Infinite sets and infinite limits		2009-03-06
		Justin pose la question : Hello, I know I have asked a similar question before but I was just wondering if set theory applies to the lim x->0, y=1/x=infinity and if so, what type of infinity would it be? Thanks a lot for your help with this question! Regards, Justin Robert Dawson and Harley Weston lui répond.
	(a x b) intersect (b x a)		2009-01-08
		sean pose la question : is it possible to have two sets such that n((a X b) intersect (b X a) =3 Harley Weston lui répond.
	A union B and A intersect B		2009-01-07
		Jim pose la question : Suppose A and B are sets and (A union B) = (A intersect B). Is it true that A=B. Penny Nom lui répond.
	The empty set		2008-09-29
		wahab pose la question : Why a null set is called a set? the definition of set includes that a set is a collection of well defined objects But a null set is having no value. Harley Weston lui répond.
	Subsets of a set		2007-10-30
		Snehal pose la question : 1. Let an denote the number of subsets of f{1,2, 3.... n}including the empty set and the set itself.) a) Show an = 2an-1 b) Guess a formula for the value of an and use induction to prove you are right Stephen La Rocque lui répond.
	Countable and uncountable sets		2007-07-24
		Mac pose la question : Hi, i tried to read few webpages related to the countably infinite and uncountable sets. Even i read few questions from this forum. But i am not convinced with this explanation. If you have any good book that explains this in layman term, please redirect me to that. 1) Can you please explain what is the difference between these too ? 2) How could you say set of Natural number and set of even numbers are countably infinite ? N={1,2,3,...} and Even= {2,4,6,...} When an element in the even set is some 2n, we will map it to 'n'.So now we have a bigger number(2n) right ? Sorry, i didn't understand that. ... Can you please help me out to understand that ? Harley Weston lui répond.
	Equality of sets		2007-07-23
		Mac pose la question : Hi, I learnt set theory recently. My teacher and few of the weblink actually give different definition for basic set. Can you please solve this ? My teacher says, {1,2,3} and {1,1,2,3} is also set. But in this link http://library.thinkquest.org/C0126820/setsubset.html it says, "A set has no duplicate elements. An element is either a member of a set or not. It cannot be in the set twice." and "{1, 2, 3} is the same as the set {1, 3, 2, 3, 1}" My question is, 1. Whether duplicates allowed in the set or not ? 2. Even if the duplicates are allowed, {1,2,3} and {1,1,2,2,3,3} are same or not ? Penny Nom and Harley Weston lui répond.
	The empty set is a subset of every set		2006-11-14
		Narayana pose la question : The empty set is a subset of every set Stephen La Rocque and Penny Nom lui répond.
	One-quarter of all 3-subsets of the integers 1,2,3....,m contain the integer 5		2006-10-09
		Hina pose la question : If one-quarter of all 3-subsets of the integers 1,2,3....,m contain the integer 5, determine the value of m. Steve La Rocque and Claude Tardif lui répond.
	Brackets and more brackets		2006-08-29
		Michelle pose la question : Feeling stupid asking but it's been awhile ... {{{2}}} ...what is this really saying ....are the outer brackets = null? Stephen La Rocque lui répond.
	Marking out a circle		2006-06-28
		Peter pose la question : given a straight line. how do i work out the off sets ( at right angles) at several intermediate points. to set out a 5.0m arc that has a 18.0m radius. Stephen La Rocque and Penny Nom lui répond.
	The cartesian product of a countably infinite collection of countably infinite sets		2006-03-25
		Geetha pose la question : Is the cartesian product of a countably infinite collection of countably infinite sets countable infinite? Penny Nom lui répond.
	A countably infinite collection of countably infinite sets		2005-02-26
		Feroz pose la question : Suppose a set can be divided into a countably infinite number of countably infinite sets.Then can the original set be considered as a countably infinite set? Penny Nom lui répond.
	B={A,{A}}		2004-09-20
		Muhammad pose la question : Let A be a set and let B = {A,{A}}. (a) Explain the elements of set B (with some example) (b) Prove that A is not a subset of B. Penny lui répond.
	Equivalent sets		2004-03-06
		A student pose la question : If A=(1,2,3,4,...) and B=(5,10,15,20,...), is A equivalent to B. Why or Why not ? Penny Nom lui répond.
	Sets		2004-01-27
		Susan pose la question : My child has the following problems to solve, and we are puzzled. 1. Compare the subset symbols to the inequality symbols of less than or greater than. 2. If A, B & C are sets such that A has 47 elements, B has 32 elements, and C is a proper subset of B, what can you say about the number of elements in the following sets: A U B? A intersect B? B U C? and B intersect C? Penny Nom lui répond.
	A problem with sets		2004-01-20
		Jason pose la question : Given that the universal set S is the set of all sports fans, and F={x|x is a football fan} B={x|x is a basketball fan} H={x|x is a hockey fan} a)Describe (F^B)' (f intersect b)' in words b)Draw a Venn Diagram and shade the region that represents the set of football fans or both basketball and hockey fans. Penny Nom lui répond.
	What is larger than infinity?		2003-01-12
		Dana pose la question : What is larger than infinity? Claude Tardif and Harley Weston lui répond.
	Combinations of 1,2,3,...,10		2002-11-27
		Gord pose la question : If I had the numbers from 1-10 how many different combinations would i have.....would it be 100....since that is 10 squared. Penny Nom lui répond.
	Two problems		2002-10-14
		Eva pose la question : a) How many different equivalence relations can be defined on the set X={a,b,c,d}? b)Show that 6 divides the product of any 3 consecutive integers. I know it is true that 6 divides the product of any 3 consecutive integers. However, i have problem showing the proof. Leeanne Boehm and Penny Nom lui répond.
	Sets and elements		2002-08-22
		Dianne pose la question : I want to know why its okay to say that, for example, 6 is an element of the set of integers, but you get counted off for saying that the set of 6 is an element of the set of integers. How come? Judi McDonald lui répond.
	Can a infinite set be smaller than another infinite set?		2001-11-29
		Carlos pose la question : Can a infinite set be smaller than another infinite set? If so why? Chris Fisher and Penny Nom lui répond.
	Cardinality of sets		2001-11-19
		Tania pose la question : Show that the cardinality of P(X) (the power set of X) is equal to the cardinality of the set of all functions from X into {0,1}. Show that (the cardinality of the natural numbers set) |N| = |NxNxN|. Show that the cardinality of the set of prime numbers is the same as the cardinality of N+ Walter Whiteley lui répond.
	Subsets of a countably infinite set		2001-11-14
		Tania pose la question : How could I show (and explain to my son) that any countably infinite set has uncontably many infinite subsets of which any two have only a finite number of elements in common? Claude Tardif lui répond.
	Subsets of the natural numbers		2001-01-30
		Christina pose la question : How do I explain why the set of natural numbers (N) cannot be equivalent to one of its finite subsets? Penny Nom lui répond.
	Derfs, Enajs and Sivads		2001-01-07
		John and Norman pose la question : All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derf nor Sivad? Penny Nom lui répond.
	Infinite sets		2000-04-12
		Brian Provost pose la question : Here's the deal: There are an infinite amount of integers (1,2,3...). Agreed? There are an infinite amount of even integers, too (2,4,6...). Agreed? By convention, infinity equals infinity. Yet common sense tells us there are obviously more integers than there are even integers. Prove this to be true mathematically. Harley Weston lui répond.
	100% on two tests		2000-02-01
		Craig and Chelsea Bruzzone pose la question : A class of 35 students took a math test and a science test. 12 students got 100% on the math test. 9 students got 100% on the science test. There were 19 students who made less than 100% on both tests. How many students made 100% on both tests? Penny Nom lui répond.

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