







Finite and infinite sets 
20190610 

Pretzie pose la question : What is Finite Set & Infinite Set? Penny Nom lui répond. 





A geometric series 
20180313 

nathi pose la question : 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. Penny Nom lui répond. 





Is infinite a number? 
20170318 

Divyansh pose la question : Is infinite a number? If yes why as i think that numbers are used for counting but infinite is undeterminable? Penny Nom lui répond. 





An infinite geometric series 
20131224 

Muhammad pose la question : The sum of an infinite geometric series is 15 and the sum of their squares is 45. Find the series Penny Nom lui répond. 





What is the smallest number? (i.e. the closest number to zero) 
20130722 

Charlie pose la question : What is the smallest number? (i.e. the closest number to zero) Harley Weston lui répond. 





1+2+4+8....= 1 
20120402 

Andy pose la question : 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=kIq5CZlg8Rg Robert Dawson lui répond. 





The sum of a series 
20111107 

Rattanjeet pose la question : 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. Penny Nom lui répond. 





Infinite Logarithmic Series 
20110808 

Sourik pose la question : 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,
Sourik Robert Dawson lui répond. 





The number of points on a line is equivalent to that of a surface 
20110324 

Gary pose la question : 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? Penny Nom lui répond. 





1/0 and 2/0 
20110211 

Dixit pose la question : How are the infinite number obtained by dividing 1 / 0 and 2 / 0 are different? Penny Nom lui répond. 





Cardinality of infinite sets 
20090901 

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. 





An infinite set 
20090807 

Islam pose la question : How can I prove that the set of all odd natural numbers is an infinite set. Thank you. Robert Dawson lui répond. 





Torricelli's trumpet 
20090729 

Gary pose la question : 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? Thanks Robert Dawson lui répond. 





InfiniteDimensional Spaces 
20090626 

Justin pose la question : Hello again, I was also just wondering (in Hilbert Space and Function Space) are there infinitedimensional spaces larger than each other in terms of cardinality? Thanks a lot for your help again!
All the Best,
Justin Victoria West lui répond. 





Prove that the set of all positive odd integers is an infinite set 
20090620 

Nazrul pose la question : How can I prove that the set of all positive odd integers is an infinite set.
Thank you in advance. Victoria West lui répond. 





An infinite number of solutions 
20090324 

Sean pose la question : 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) = 0 Harley Weston lui répond. 





An integral from 1 to infinity 
20090124 

Ray pose la question : Determine the area bounded by the xaxis and the curve y=1/(x^2) from x=1 to x=infinity.
A. 1.00
B. infinity
C. indeterminate
D. 2.00 Harley Weston lui répond. 





0.151515...=15/99 
20080908 

Emma pose la question : 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
Emma Penny Nom lui répond. 





algebra 
20080731 

Eric pose la question : Would you please solve & explain this equation to me: x^2+2x=x(x+2)?
Thank you Penny Nom & Stephen La Rocque lui répond. 





33+33+3.........up to infinite terms = ? 
20080425 

Jatin pose la question : 33+33+3.........up to infinite terms = ? Stephen La Rocque lui répond. 





Two equations in two unknowns 
20070922 

Mary pose la question : 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=0 Stephen La Rocque and Leeanne Boehm lui répond. 





Countable and uncountable sets 
20070724 

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. 





What happens when you have zero's on both sides? 
20070605 

Lily pose la question : 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? Stephen La Rocque and Penny Nom lui répond. 





Countable and uncountable sets 
20070213 

piyush pose la question : 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 set Penny Nom and Claude Tardif lui répond. 





Sigma from 0 to infinity of (n^3 / 3^n) 
20061115 

Cedric pose la question : 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? Penny Nom lui répond. 





The cartesian product of a countably infinite collection of countably infinite sets 
20060325 

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 
20050226 

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. 





x^x^x^x^... 
20040123 

Ryan pose la question : 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 2 Penny Nom lui répond. 





X.9999... and X+1 
20030823 

David pose la question : 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??? Penny Nom lui répond. 





What is larger than infinity? 
20030112 

Dana pose la question : What is larger than infinity? Claude Tardif and Harley Weston lui répond. 





Repeating decimals 
20030108 

A student pose la question : If k=.9repeating, and 10k=9.9repeating then 10kk=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? Penny Nom lui répond. 





A bouncing ball 
20021214 

Eman pose la question :
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.
Penny Nom lui répond. 





Can a infinite set be smaller than another infinite set? 
20011129 

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 
20011119 

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 
20011114 

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. 





2=the square root of (2 + the square root of (2 + the square root of (2 +...))) 
20011105 

Cynthia pose la question : 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, ....... Penny Nom lui répond. 





An infinite series 
20001216 

John pose la question : summation(n=1 to infinity)[n sin(1/(2n))]^{n} Harley Weston lui répond. 





Infinite Geometric Series 
20001110 

Sam Carter pose la question : 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. Harley Weston lui répond. 





Infinite sets 
20000412 

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. 





A system of equations in five unknowns 
20000320 

Will pose la question : 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 . . . Penny Nom lui répond. 





Limited area and unlimited perimeter. 
19971128 

Rosa pose la question : 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! Harley Weston lui répond. 

