







Is infinite a number? 
20170318 

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. 





An inequality 
20140125 

From LANELL: this is a problem to solve: 1/3 + 2/7 >=x/21  part of the answer is (oo)
not exactly that similarit is on a calculator as a symbol sure you know what it is I am talking about the x will be a number Answered by Penny Nom. 





Extended real numbers 
20111212 

From Justin: Hi there, I was wondering does +infinity=+infinity in the extended real number system? Basically, I was wondering does +infinity=+infinity since infinity and any extended real number (except +infinity) are less than +infinity?
Sincerely,
Justin Answered by Robert Dawson. 





1 divided by 0 and infinity 
20111024 

From ritika: we say that one divided by zero gives us infinity, then why zero multiplied by infinity does not gives us one????????????? Answered by Robert Dawson. 





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

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 
20110211 

From Dixit: How are the infinite number obtained by dividing 1 / 0 and 2 / 0 are different? Answered by Penny Nom. 





Ascribing a value to 1/infinity 
20091119 

From Jack: Hello, and, in advance, thanks for answering.
I came across the problem of ascribing a value to 1/∞ (one divided by infinity) recently, I heard many things:
that it is infinitesimally small (i.e. .0000000000...1 the most intuitive), that it is 0 (the most ludicrous of them
all in my mind), and that it is not definable (which makes the most sense, although is a bit of a let down).
I know that lim (x>∞) 1/x = 0 and this is often used as an argument for all three possibilities. So
what's the ruling on this? And, I know this question has already been answered, but for a little modification;
is there any way to prove the answer that seems to be the most prevalently used (not definable as ∞ is a concept)
with mathematical logic? Or is it just because of the definition of ∞? Answered by Robert Dawson. 





Cardinality of infinite sets 
20090901 

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,
Brian Answered by Victoria West. 





An infinite set 
20090807 

From Islam: How can I prove that the set of all odd natural numbers is an infinite set. Thank you. Answered by Robert Dawson. 





The extended real number system 
20090630 

From Justin: Hi again, thanks a lot for answering my previous question! I was also just wondering again if the extended real number system has a potential or actual infinity because it includes positive infinity as a point that exists at the end of it?
All the Best,
Justin Answered by Robert Dawson. 





Potential infinity and actual infinity 
20090629 

From Justin: Hi there, I was just wondering what is the difference between the potential infinity and actual infinity in math? Thanks a lot for your help with this question!
All the Best,
Justin Answered by Robert Dawson. 





Dividing infinity by infinity 
20090624 

From Justin: Hello again, I just had one other question nagging question about infinity. I read this article on "Types of Infinity" on Paul Hawkins calculus website and he stated that one infinity cannot be divided by another or that the answer is inderterminate because fundamentally infinity comes in different sizes with respect to infinite sets and that this applies also to calculus. And so I was wondering (if this is true) is this why when you divide infinity by infinity (in the extended real number system) the answer is indeterminate since fundamentally one inifnity is larger than another like in infinite sets or is there another reason? Thanks sooo much for answering my question again! I greatly appreciate it!
All the Best,
Justin Answered by Robert Dawson. 





Is one Infinity larger than another in the extended real number system? 
20090624 

From Justin: Hello there, I was wondering if one infinity is larger than another in the extended real number system (just like in the transfinite ordinals and cardinals with respect to infinite sets) or are all infinities the same size in the extended real number system? Thanks sooo much for answering my question! I greatly appreciate it!
All the Best,
Justin Answered by Robert Dawson. 





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

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 
20090603 

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,
Justin Answered by Robert Dawson and Harley Weston. 





Infinity and AlephNull 
20090414 

From Justin: Yes, I am reading the Paul Halmos book on Set theory, thanks for telling me how to get it! I was just wondering from your last answer though if the positive real infinity of calculus then corresponds to Alephnull? I am sorry if this is a similar question to the one I asked before but I was just wondering about this!
All the Best,
Justin Answered by Robert Dawson. 





Positive real infinity and Alephnull 
20090409 

From Justin: Hello, I was just wondering why does the positive real infinity correspond to Alephnull? Thanks a lot for answering my question!
Justin Answered by Ami and Robert Dawson. 





Infinite sets and infinite limits 
20090306 

From Justin: 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 Answered by Robert Dawson and Harley Weston. 





More on cardinal numbers 
20090218 

From Justin: Hello again, I was just wondering that since the rules of Cantor's cardinal numbers in set theory do not apply to the infinity obtained by limits in calculus (ex. x>0, y=1/x=infinity), does that mean that this infinity is the largest quantity in both calculus and mathematics?
Justin Answered by Robert Dawson. 





How can other infinites can be larger than each other? 
20090217 

From Justin: Hello again, I was just wondering even in the context of set theory, how can other infinites can be larger than each other, I thought infinity itself is the largest possible quantity?
Justin Answered by Victoria West and Robert Dawson. 





More on infinity and Set Theory 
20090217 

From Justin: I greatly appreciate your help I was just wondering from your previous answer, why doesn't Cantor's cardinal numbers in set theory apply to the limit x>0, y=infinity?
Justin Answered by Robert Dawson. 





Infinity and Set Theory 
20090217 

From Justin: I was just wondering is the limit x>0, y=1/x=infinity, the biggest uncountable infinity according to Cantor's cardinal numbers in set theory?
Justin Answered by Robert Dawson. 





An integral from 1 to infinity 
20090124 

From Ray: 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 Answered by Harley Weston. 





Limit as it Approaches Infinity 
20080729 

From mary: i was trying to find the limit of this problem
the limit as x approches infinity of x minus cosx divided by x
lim xcosx/x
x>oo Answered by Harley Weston. 





1/2 of infinity 
20080516 

From Pamela: Hello. My question was posed to me by my husband, who says he knows the answer and that there is an answer....I have tried to research it myself but to no avail. Here is the question, as he posed it to me.
?? = 1/2 of infinity. Answered by Stephen La Rocque, Penny Nom and Claude Tardif. 





Zero divided by infinity 
20080503 

From ANNE: There was a question about what do you get when you divide Zero by infinity. There was an example using Potatoes. Could someone please explain a little bit more in detail, so that I can help my son who has Schizophrenia understand. He is big into Mathematics and is consumed by this question.
Thankyou so much,
Anne Answered by Penny Nom. 





Limits as x approaches a constant 
20070625 

From Mac: can you please tell me what is the reason they say "denominator is a negative quantity"
in the solution 11 and "denominator is a positive quantity" solution 10 ??
If i guess correctly, for solution 10, its because of x^2 in the denominator. Answered by Penny Nom. 





1/infinity and 1/0 
20060304 

From Evan: I was thinking the other day when i was in math class that when you divide 1 by say n you'll get 1/n. As the value of n increases the smaller the number you get. So if you divide 1/infinity would that equal zero? And if that is true then would 1/0=infinity be true also? Answered by Penny Nom. 





0.999..., asymptotes and infinity 
20041217 

From Mike: My Name is Mike and I teach high school. I had a student ask me to explain why .9 repeating is equal to 1. Then he asked me about an asymptote, or why a parabola or any other curve for that matter can continually approach a value (like 1) and yet never attain a value of 1. He is thinking that these two should represent the same concept and yet they contradict each other. Do you have a solid explanation for him? Of by the way he is a 7th grader. Great little thinker!!!!! Answered by Claude Tardif and Harley Weston. 





Different infinities 
20040527 

From Plober: How can I explain to a friend (in a bar, using as a pen and a paper napkin) that the integer's infinity is 'smaller' than the irrationals's one? The demo I tried was that you couldn't match the integers with the real numbers between 0 and 1 (that 0.xxxxx replacing the Nth number from a different one... that demo), but she used my argument >: saying that you can add one to the integer's infinite, and the number I was creating was only one more...
I can't think of any other way, and I KNOW the real's cardinality is greater than the integer's one Answered by Claude Tardif and Penny Nom. 





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

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 2 Answered by Penny Nom. 





Dividing zero by infinity 
20040108 

From Jason: What do you get when dividing zero by infinity? Our Calculus teacher was pretty sure that the expression was indeterminate from. However, if this is so...Why? Zero divded by any number (except zero) is zero, true. Any number (except infinite) over infinite is zero. So, why isn't Zero divided by infinite zero. A simpler way if I had 4 potatoes and was to split them among 2 friends, each friend would get 2 potatoes. However, if I had 0 potatoes and split them a infinite number of ways, each person would still have 0. Explain please! Answered by Penny Nom. 





0/0 
20030925 

From Thomas: How is 0/0 ever defined. Answered by Penny Nom. 





What is larger than infinity? 
20030112 

From Dana: What is larger than infinity? Answered by Claude Tardif and Harley Weston. 





Repeating decimals 
20030108 

From A student: 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? Answered by Penny Nom. 





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

From Carlos: Can a infinite set be smaller than another infinite set? If so why? Answered by Chris Fisher and Penny Nom. 





Asymptotes 
20011109 

From Frank:
given the function: f(x) = (x^{2}) / (x1) the correct answer to the limit of f(x) as x approaches infinity is: y = x+1 all math references point to this answer and the method they all use is long division of x1 into x^{2} however if one were to multiply both the numerator and denominator by 1/x and then take the limit, one gets: y=x how can the descrepency between the two answers be explained? Answered by Chris Fisher and Penny Nom. 





Infinite sets 
20000412 

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. 





Infinity 
19990908 

From Richard Tracy: In order to transverse from point A to point B one must first cross the halfway point (C). Additionally....One must also pass another halfway point labeled (D) in order to get to the halfway point of (C). There is also point (E) which is the halfway point between A and D. We have to assume that there are an infinite amount of halfway points points between (A) and (B). My understanding of infinity is something that goes on forever. But how can one expect to traverse over infinity in a finite amount of time? Will we never reach (B)? Answered by Walter Whiteley. 





Infinity Symbol 
19990713 

From Mark E. Kelly: There is a symbol that looks like a sideways 8 that is used to represent infinity. Does it have a name? Answered by Doug Farenick and Penny Nom. 





Indeterminate forms 
19981211 

From R. Dixon: What is the correct evaluation of infinity/0 ? I've checked three different math sites. One says definitively, that infinity/0 is "not" possible. Another states that infinity/0 is one of the indeterminate forms having a large range of different values. The last reasons that infinity/0 "is" equal to infinity. Answered by Walter Whiteley and Harley Weston. 





Limited area and unlimited perimeter. 
19971128 

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. 





Division by zero 
19970214 

From Linda Hood: I am a college student and have been asked to explain and figure out why we can't divide by zero. Answered by Chris Fisher. 

