Infinity Definition and 988 Threads

I am interested in learning more about this concept where 1/0 can in this context be defined as infinity, however, I hear that infinity times 0 still will not reproduce 1 in this context. I have looked up some youtube mobius transformations and have read that "A Möbius transformation is a...

Homework Statement Evaluate lim (1+a/x)^x (that's limit as x tends to +infinity, sorry don't know how to latex that) Homework Equations The Attempt at a Solution Stumped. Having that x exponent has my confused. As x tends to infinity I know what's inside the brackets will tend to one, but the...

Hi all, I'm stuck on this problem, I can't solve it :confused: Sum(from 1 to infinity) of 8 / x^2(4+ln(x)) Does anybody have the fainest idea of how to solve? Thanks all

In ZF, the axiom of infinity says that the set of natural numbers exists. I was wondering if there was a (finitist?) weakening of ZF that included the axiom "the class of natural numbers exists".

[SOLVED] Voltage Query Homework Statement An insulating spherical shell with inner radius 25.0 cm and outer radius 60.0 cm carries a charge of + 150.0 \mu C uniformly distributed over its outer surface. Point a is at the center of the shell, point b is on the inner surface and point c is on...

Why does \lim(1+\frac{1}{x})^x = e x->\infty

Homework Statement \lim x-> \infty [x+1-ln(x+1)] Homework Equations The Attempt at a Solution How does one evaluate this? I don't know how to use L'Hopital's rule on this and I have infinity- infinity, which is indeterminate. Thanks!

I'm looking for help with my conceptual understanding of part of the following: 1) If a series is convergent it's nth term approaches 0 as n approaches infinity This makes perfect sense to me. 2) If the nth term of a series does not approach 0 as n approaches infinity, the series is...

Does any formula gives invalid results at infinity or zero compared to other values in the formula? I tried as an example some calculus at normal values gives answers and at infity and zeros the rule is broken... I think it is a must to formulate 0 with infinity and i don't know how...

Homework Statement 1) Find the cardnality of the set of constructible angles whose cosine is a) irrational b) rational 2. The attempt at a solution For the other questions I have posted my attempt, but for this one I really have no clue... Could someone please give me some general...

I am still struggling with the topic of cardinality, it would be nice if someone could help: 1) http://www.geocities.com/asdfasdf23135/absmath2.jpg In the solutions , they said that{y=ax+b|a,b E R} <-> R2. But I am wondering...what is the actual mapping that gives one-to-one...

1) Consider the xy-plane. Find the cardinality of the set of constructible points on the x-axis. Attempt: Every constructible number is algebraic (i.e. Let A=set of algebraic numbers, C=set of constructible nubmers, then C is a subset of A) and A is countable. => |C|<|A|=|N|...

[b]1. Homework Statement [/bProve Prove: If the limit as x goes to a of f(x)=infinity, then lim as x goes to a of 1/(f(x) =0 Homework Equations Need to show with a delta-epsilon proof The Attempt at a Solution using the definition, lim as x goes to a f(x)=infinity means that for any...

Say a function f and its derivative are everywhere continuous and of exponential order at infinity. F(s) is the Laplace transform of f(x). I need to find the limit of F as s goes to infinity. I use the integral definition of the Laplace transform and the fact that f is of exponential order...

Homework Statement Velocity of an electron that falls to r from infinity? An electron falls from infinity to r=10^-8m from a charge q1=4.8x10^-19C. What is the velocity of the electron? Homework Equations U=q1V V=kq2/r The Attempt at a Solution Potential energy change U...

These are some related questions in my mind, though I am rather confused about them. 1. What does \infty at the "end" of the real number line have to do with \aleph_0, the cardinality of the integers, and C, the cardinality of the continuum? Is \infty equal to one or the other (if such a...

i got into a minor argument with a buddy of mine, he said the derivative of infinity is zero, and i argued that you can't take the derivative of infinity. my argument was that by definition of derivative there isn't a function that can equal infinity, so you can't take the derivative of it...

Homework Statement I'm a bit puzzled with a limit, as is my teacher. We came across a question that could be both factored or rationalized, but when factored, the answer is different. Perhaps someone has an explanation? Here it is. lim ((√x^2+4x)-x) x->∞ I'm not going to rationalize...

Homework Statement limit approaching infinity: (arcsin(x))/(x) = 0 Question is: Why? The 'Sandwich Theorem' 0=[(arcsinx)/x]=0 gives this solution, but looking at the graph of (arcsinx)/x , this appears impossible. Homework Equations lim x->OO [arcsin(x)] - {DNE) lim x->OO...

Show that: lim (1-1/n)^n=1/e n->infinity I don't really know where to begin...

Help, I am infinitly confused :) When solving the limit for this type and factoring the largest power of a variable in the polynomial in order to make its coefficient become a limit multiplied by another limit of Infinity I get lost. I just do not understand how (Infinity)(5 + Infinity +...

lim as x goes closer to minus infinity. x^4 + x^5 now visibly the answer is minus infinity since the equation are simple. But aside from saying x^5 is bigger then x^4 could there be anything else to do ?

lim (x^2 - x) as x---> inf. I thought it was in indeterminate form inf. - inf. but my friend said that it's just inf. please help

Let me preface this as this is my first post on this forum. I'm a physics major at Virginia Tech and I've lurked the forum for a while to help understand concepts that may not be intuitive initially. I'm stuck on this one concept, so I decided to give posting a shot. Without further ado...

What is infinity mathematically? What type of number is infinity, i.e., which number system does it belong to? Is there any good books/text books on infinity and its weirdness? I am hoping for a book that has no philosophy, mathematics of infinity Thanks,

Homework Statement \lim_{x \rightarrow \infty} 2x+1-\sqrt{4x^2+5} The Attempt at a Solution i am wondering if this method that i used is correct. i get the correct answer but i ahaven't see it in the textbook or on the net. am i doing something that shouldn't be done? using...

Homework Statement Find limit as n -> infinity [ (n+1)^2 ] / [ \sqrt{}3+5n^2+4n^4 ] Homework Equations L'Hopital won't do the job, I think. The Attempt at a Solution It's something really small I'm just completely missing.

Let n be any number. infinity + n = infinity n = infinity - infinity n = undefined !...?

I have just starting getting into this stuff over the last few years and I recently read an article about the newest theory on the creation of our universe. If our Universe was created by the colliding of two branes in another dimension and eventually once all the energy in our Universe has...

Homework Statement Consider the function, {{\vec{F}}(r)} = {\int_{-\infty}^{\infty}}{{\vec{f}}(r)}{\times}{d{\vec{r}}} Is the following true?, {\int_{-\infty}^{\infty}}{{\vec{f}}(r)}{\times}{d{\vec{r}}} = {2}{\int_{0}^{\infty}}{{\vec{f}}(r)}{\times}{d{\vec{r}}} Homework...

Homework Statement Integral from 1 to infinity of 1 / xln(third root of x) 2. Homework Equations n/a 3. The Attempt at a Solution I tried to find if it diverged and then got lost after that Homework Equations The Attempt at a Solution

Homework Statement Find the limit as n tends to infinity of xn = (n^2 + exp(n))^(1/n) Homework Equations maybe use ( 1 + c/n )^n tends to exp(c) The Attempt at a Solution I know that inside the barckets are both inceasing and the 1/n makes it decrease but how do i find out which...

Homework Statement 2 Questions, both find xn as n tends to infinity. http://img229.imageshack.us/img229/5154/scan0002un5.th.jpg Homework Equations The Attempt at a Solution Have attempted question one but am unsure if (1/n)log(n^2) tends to 0, and if it does do i need to prove it? I don't...

If ∑ C An (n from 1 to infinity) converges, and C in Real, then ∑ C An is convergent with : ∑ C An =C ∑ An (n from 1 to infinity) .. why?

I am doing a question that goes like this Lim of sqrt(x) * sine(1/sqrt(x)) as x --> infinity = ? what i determined was as x --> infinity 1/sqrt(x) would approach zero there for sine of 1/sqrt(x) would approach 1 there fore 1 * sqrt(infinity) would be infinity. however the answer says it is 1...

The problem is The limit as x approaches pos infinity ln(square root of x + 5) divided by ln(x) In the numerator only x is under the square root. I'm having trouble getting to this answer. If someone can take a look I would really appreciate it.

Please help, i take out n^2 top and bottom so end up with 0 as demominator... Find lim (n to infinity) xn xn = (n^2 + log n)/(2n^3 - 1)^(1/2) ...?

Here's an idea that I have been working on for the past few months. After weeks of writing out idea after idea about the universe and other universes I have reason to believe that there is an infinite number of universes contained in infinity itself. Here's the idea broken up: There is one...

Could some one please explain to me 2 things 1) I have seen integrals that are between 0 and ∞ and also between -∞ and ∞. What does this mean 2) I have also seen sigma series (∑) between n=1 and ∞. What doe this mean Thanks heaps

Why is it that a circle with an infinitly large radius is a line?

ok I am confused when x->negative infinity or positive infinity. for example lim (5x^3+27)/(20x^2 + 10x + 9) x-> negative infinty heres what i think, i want to know if i have the right idea or not. - so since the top exponent is larger then the denominator the lim DNE and so i...

Spare me the ridicule for asking a stupid question, I'm just your average guy trying to comprehend his environment. I do my best to understand the origins and workings of the universe but no matter what path I take I will end up facing an infinity of one form or other. Ok here goes. I have...

Homework Statement \lim_{\substack{x\rightarrow \infty}}f(x)=\sqrt{3x^2+8x+6}-\sqrt{3x^2+3x+1} Homework Equations The Attempt at a Solution I truly have no idea how to solve this. I know I need to get x in some rational form like 5/x but I'm not sure how to do this with the...

Homework Statement f(x) = sqroot(ax^2 + 1 ) - x find all the different limits in + infinity that f can have with all the different "a" values Homework Equations The Attempt at a Solution i don't know if i did something wrong here : - if a = 0 then f = 1 - x, limit : -...

How big is Infinity ? like eletron is considered the samllest thing ever, wouldn't that be the lowest value of negative inifinty in teh size of things but overall how big or small is infinity ?

I understand that infinity - X = infinity. However, what I don't understand is this. If I have: infinity - 1 = infinity, AND infinity - 5 = infinity, is the first infinity larger than the second? If so, how can that be? Because they are infinite, how can one really be larger than the...

If infinity were to be possible, it would seem that nothing in it's surrounding environments could be segmented or finite. How do we record segments of something that is infinite like for example time? It's almost as if infinity is really points of end, causing new beginnings. Thus causing an...

We know that anything divided by zero is 'undefined' or equal to infinity. Is it not possible to define in anyway such indeterminate quantities? The concept of zero basically refers to 'nothingness' or 'void', but that indeed has utmost importance in writing numbers. If you consider a general...

Can someone give me a hint on how to evaluate the following limit? \stackrel{lim}{T\rightarrow\infty} (Texp(c/T) - T) I tried multiplying the numerator and denominator by the conjugate (because that sometimes helps) and got: (T^2exp(2c/T) - T^2) / (Texp(c/T) + T) But I'm not sure what I...

Perhaps some consensus can be arrived at in regard to what infinity is. After that, perhaps its nature can then be discussed. One approach to defining infinity is to first define what finite means and then say something is infinite if it is not finite. Rather than define infinity by what it...