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 Finite and infinite sets 2019-06-10 From Pretzie:What is Finite Set & Infinite Set?Answered by Penny Nom. A geometric series 2018-03-13 From nathi:Hi I am really struggling with this question please help !!!! a pohutukawa tree is 86 centimetres when it is planted. in the first year after it is planted , the tree grows 42 centimetres in height.Each year the tree grows in height by 95% of the growth of the previous year. assume that the growth in height of the pohutukawa tree can be modelled by a geometric sequence. A)find the height of the tree 5 years after it is planted and figure out the maximum height the pohutukawa tree is expected to reach in centimetres. The maximum height part is not answered.Answered by Penny Nom. Is infinite a number? 2017-03-18 From Divyansh:Is infinite a number? If yes why as i think that numbers are used for counting but infinite is undeterminable?Answered by Penny Nom. The integral of a sum 2016-03-10 From Rahul:How to solve definite integral of a sum. The specific problem is as follows, Integral of ( 1+ sum of x^k, k=1 to k=n), x=0 to x=b *dx. The answer is b + sum of b^(k)/k, k=2, to k=n+1. I understand only the integral of first term. But integral of the sum I do not understand at all.Answered by Penny Nom. An infinite geometric series 2013-12-24 From Muhammad:The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the seriesAnswered by Penny Nom. What is the smallest number? (i.e. the closest number to zero) 2013-07-22 From Charlie:What is the smallest number? (i.e. the closest number to zero)Answered by Harley Weston. We can't write sinx and cosx as a finite polynomial. 2013-03-31 From rimoshika:prove that we can't write sinx and cosx as a finite polynomial.Answered by Walter Whiteley. 1+2+4+8....= -1 2012-04-02 From Andy:In this minutephysics video, it's claimed that 1+2+4+8....= -1 Is this true, and if so, how? < href="http://www.youtube.com/watch?v=kIq5CZlg8Rg">http://www.youtube.com/watch?v=kIq5CZlg8RgAnswered by Robert Dawson. The sum of a series 2011-11-07 From Rattanjeet:Find the sum of 1(1/2) + 2(1/4) + 3(1/6) + 4(1/6)(3/4) + 5(1/6)(3/4)2 + 6(1/6)(3/4)3+ ... where 1/6 + (1/6)(3/4) + (1/6)(3/4)2 + ... constitutes a geometric series.Answered by Penny Nom. Infinite Logarithmic Series 2011-08-08 From Sourik:Dear Expert, In my Amithabha Mitra and Shambhunath Ganguly's "A Text Book of Mathematics" I found the formula of log (1+x) where the base is e and x lies in between -1 and +1.As I want to learn Mathematics,I am not satisfied with the mere statement of the formula.Please help giving me the full proof. Thanking you, SourikAnswered by Robert Dawson. The number of points on a line is equivalent to that of a surface 2011-03-24 From Gary:I I was reading about how the number of points on a line is equivalent to that of a surface. This was done by taking any point on a line then taking alternating digits and making them as points on an x and y axis therefore points on a surface.The problem is as i see it if you just take a line then hold it over a surface you have just put the points on the line in a one to one correspondence with the points directly under it on the surface.Now you have all the rest of the surface which cannot be mapped onto the line since it is already used up.What am i missing?Answered by Penny Nom. 1/0 and 2/0 2011-02-11 From Dixit:How are the infinite number obtained by dividing 1 / 0 and 2 / 0 are different?Answered by Penny Nom. Cardinality of infinite sets 2009-09-01 From Brian: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, BrianAnswered by Victoria West. An infinite set 2009-08-07 From Islam:How can I prove that the set of all odd natural numbers is an infinite set. Thank you.Answered by Robert Dawson. Torricelli's trumpet 2009-07-29 From Gary:I was reading about torricelli's trumpet which is described by the equation1/x which is then rotated around the x axis which results in a figure which looks like a trumpet. Now in order to find the volume the integral 1/x^2 dx is used which diverges when integrated so the volume is finite.However if you integrate 1/x dx which is the formula on the plane the answer diverges. Now if you took an infinite area then rotated it around the x axis shouldn't you get an infinite volume? Notice the area I am talking about is under the line 1/x not the surface area of the trumpet which is what the painters paradox is about What am I missing? ThanksAnswered by Robert Dawson. Infinite-Dimensional Spaces 2009-06-26 From Justin:Hello again, I was also just wondering (in Hilbert Space and Function Space) are there infinite-dimensional spaces larger than each other in terms of cardinality? Thanks a lot for your help again! All the Best, JustinAnswered by Victoria West. Prove that the set of all positive odd integers is an infinite set 2009-06-20 From Nazrul:How can I prove that the set of all positive odd integers is an infinite set. Thank you in advance.Answered by Victoria West. Omega 1 2009-06-03 From Justin:Hello there, I was just wondering if the infinity in the extended real number system is the same as w1 (or Omega 1, the order structure of the real numbers) in the transfinite ordinals? Thanks so much for your help with this question, I really appreciate it! Sincerely, JustinAnswered by Robert Dawson and Harley Weston. An infinite number of solutions 2009-03-24 From Sean:this is a linear equations problem; first: 3535.5 + Fbd (.866) + Fbc (.5) - Fab (.5) = 0 and -3535.5 - Fab (.866) - Fbc (.5) - Fbd (.5) = 0Answered by Harley Weston. A definite integral 2009-02-09 From Mathata:Evaluate: integral from 0 to 1, x^2 e^x^3dxAnswered by Harley Weston. An integral from 1 to infinity 2009-01-24 From Ray:Determine the area bounded by the x-axis and the curve y=1/(x^2) from x=1 to x=infinity. A. 1.00 B. infinity C. indeterminate D. 2.00Answered by Harley Weston. The integral of f(x)dx and the integral of f(x-4)dx 2009-01-02 From Katie:Calculus: If the definite integral from -2 to 6 of f(x)dx=10 and the definite integral from 2 to 6 of f(x)dx=3, then the definite integral from 2 to 6 of f(x-4)dx= ? I don't understand how to solve definite integrals when the function has something more than just x inside the parenthesis such as f(4-x).Answered by Robert Dawson. 0.151515...=15/99 2008-09-08 From Emma:This week, my Algebra teacher told us about the pattern between infinitely repeating decimals and their corresponding fractions. (ex. .2222222...= 2/9, .151515...=15/99, 456456456...=456/999, etc.) I was just wondering the reason why this pattern occurs. Is there a certain element that causes this pattern to occur? Thanks -EmmaAnswered by Penny Nom. algebra 2008-07-31 From Eric:Would you please solve & explain this equation to me: x^2+2x=x(x+2)? Thank youAnswered by Penny Nom & Stephen La Rocque. The mean and variance 2008-06-05 From Donny:An investment will be worth \$1,000, \$2,000, or \$5,000 at the end of the year. The probabilities of these values are .25, .60, and .15, respectively. Determine the mean and variance of the worth of the investment.Answered by Harley Weston. 3-3+3-3+3.........up to infinite terms = ? 2008-04-25 From Jatin:3-3+3-3+3.........up to infinite terms = ?Answered by Stephen La Rocque. Two equations in two unknowns 2007-09-22 From Mary:Having problems doing this problem, looking for a solution with the work. I would like to see how you got your answer, to see what I was doing wrong. solve using the substitution method, is there "no solution" or "infinitely many solutions" 4x+y=4 2x+8y=0Answered by Stephen La Rocque and Leeanne Boehm. More on the cardinality of sets 2007-07-27 From Mac:Can you please help me to find and verify whether the following are finite, countably infinite and uncountable ?Answered by Harley Weston. Countable and uncountable sets 2007-07-24 From Mac: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 ?Answered by Harley Weston. What happens when you have zero's on both sides? 2007-06-05 From Lily:On the substitution method what happens when you have zero's on both sides of the equation? Is that considered no solution or infinitely many?Answered by Stephen La Rocque and Penny Nom. Countable and uncountable sets 2007-02-13 From piyush:we se that union of countably infinite no of sets having countably infinite number of elements is a countable set we can express p(n) (i.e power set of natural number) as a union of countable infinite number of sets i.e p(n)=s1Us2Us3..... where s1=null s2={1,2,3,4,5..........} s3={{1,1},{1,2},{1,3},..............{2,1},{2,2}........} using the same statement can we prove that power set of natural number is a infinit countable setAnswered by Penny Nom and Claude Tardif. Sigma from 0 to infinity of (n^3 / 3^n) 2006-11-15 From Cedric:I'm wondering how you would find if this series converges or diverges? Sigma from 0 to infinity of (n^3 / 3^n) Does the n^3 dominate, or does the 3^n dominate? What about higher powers like n^10 / 10 ^ n ? Which one would dominate then?Answered by Penny Nom. The cartesian product of a countably infinite collection of countably infinite sets 2006-03-25 From Geetha:Is the cartesian product of a countably infinite collection of countably infinite sets countable infinite?Answered by Penny Nom. A countably infinite collection of countably infinite sets 2005-02-26 From Feroz: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?Answered by Penny Nom. x^x^x^x^... 2004-01-23 From Ryan:you have a number say x and it is to the power of x which is to the power of x and so on infinite times like x^x^x^x^x^x^x^... i have to figure out what x is so that the answer is always 2Answered by Penny Nom. X.9999... and X+1 2003-08-23 From David:I have read your answers to the questions on rational numbers, esp. 6.9999... = ? and still have a question: The simple algebraic stunt of converting repeating decimals to rational numbers seems to work for all numbers except X.999999.... where X is any integer. The fact that the method yields the integer X+1 in each case seems to violate the completeness axiom of the real numbers, namely that there is no space on the number line which does not have an number and conversely that every geometric point on the number line is associated with a unique real number. In the case of 3.999... for example, it seems that both the number 4 and the number 3.9999.... occupy the same point on the number line. How is this possible???Answered by Penny Nom. Finite differences 2003-02-10 From Jenny:I need to find a formula that will work with any number. I am finding the volume of a 3d cross- shape. Here are my results so far: ```Term Number 0 1 2 3 4 5 nth term 1 7 25 63 129 231 1rst diff 6 18 38 66 102 2nd diff 12 20 28 36 3rd diff 8 8 8 ``` I can't seem to find a formula that will work with any number. Any help would be much appreciated. Answered by Penny Nom. What is larger than infinity? 2003-01-12 From Dana:What is larger than infinity?Answered by Claude Tardif and Harley Weston. Repeating decimals 2003-01-08 From A student:If k=.9repeating, and 10k=9.9repeating then 10k-k=9k, k=1 therefore .9repeating=1 and 1/3=.3repeating 3x1/3=.3repeatingx3, 3/3=.9repeating, therefore 1=.9repeating It would seem to me that .9repeating approaches one but never quite makes it. Can you clarify? Answered by Penny Nom. A bouncing ball 2002-12-14 From Eman: Q : When a childís ball is dropped from a height h metres on to a hard, flat floor, it rebounds to a height of 3/5h metres. The ball is dropped initially from a height of 1.2m. Find the maximum height to which the ball rises after two bounces. Find the total distance that the ball has traveled when it hits the floor for the tenth time. Assuming that the ball continues to bounce in the same way indefinitely, find the total distance that the ball travels. Answered by Penny Nom. Can a infinite set be smaller than another infinite set? 2001-11-29 From Carlos:Can a infinite set be smaller than another infinite set? If so why?Answered by Chris Fisher and Penny Nom. Cardinality of sets 2001-11-19 From Tania: 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+ Answered by Walter Whiteley. Subsets of a countably infinite set 2001-11-14 From Tania: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?Answered by Claude Tardif. 2=the square root of (2 + the square root of (2 + the square root of (2 +...))) 2001-11-05 From Cynthia:justify algebreically, that: 2=the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + the square root of 2 + and so on, ....... Answered by Penny Nom. Finite differences 2001-10-08 From Murray:My name is Murray and I am a 10th grade student. Me and my friend have recently discovered and proved a theorem of a relitively advanced nature. It is that the the nth difference of an nth degree equation = n! times the coefficient of the highest power. One of my teachers said this theorem is part finite and that she thinks she has seen it before, but she does not remember what it is called, at what level it is taught, who discovered it or when it was invented. I would greatly appretiate answers to any of these questions.Answered by Chris Fisher. Subsets of the natural numbers 2001-01-30 From Christina:How do I explain why the set of natural numbers (N) cannot be equivalent to one of its finite subsets?Answered by Penny Nom. An infinite series 2000-12-16 From John:summation(n=1 to infinity)[n sin(1/(2n))]nAnswered by Harley Weston. Infinite Geometric Series 2000-11-10 From Sam Carter:I ran into a problem when studying how to find the sum of an infinite geometric series. My math book attempts to explain the concept by giving formulas involving sigma and |r|, but it does not really explain how to go about finding the sum of an infinite geometric series. If you could either help me with this or point me in the direction of an informative website that could help me, I'd appreciate it. Answered by Harley Weston. An indefinite integral 2000-05-03 From Bonnie Null:I am to find the indefinite integral of: (ex - e-x)2 dxAnswered by Claude Tardif. Infinite sets 2000-04-12 From Brian Provost: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. Answered by Harley Weston. A system of equations in five unknowns 2000-03-20 From Will:I have been having some problem with the following question for some time. I would appreciate any help on solving the problem or a solution. Q: Assume that a system of equations in the unknowns x1, x2, x3, x4 and x5 when converted to row echelon form gives ...Answered by Penny Nom. Limited area and unlimited perimeter. 1997-11-28 From Rosa:There is a figure, it has unlimited perimeter but has limited area , what is the figure and how to draw it ? Thank you very much!Answered by Harley Weston. A Finite Math Question. 1997-09-07 From Angela L.:How many three-digit numbers can be formed using only the numbers 1 to 7 if the number 2 must be included?Answered by Penny Nom.

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