Infinity Definition and 970 Threads

I have a problem with the concept of a singularity, defined as something that has a property which is infinite. Infinities do not belong in our reality, and in my opinion are just hints that our understanding of the phenomenon is incomplete or wrong. From my understanding, during the collapse...

If we choose rational numbers to represent points on a line then there will be gaps on the line and consequently the plane will be full of holes. Then we cannot say that two non-parallel line must intersect on a point (because they may meet at the gaps). So obviously we need point arranged more...

Show that $\lim_{{x}\to{0}}$ $\frac{1}{x}$ does not exist? Please tell me how to make LHL and RHL for this? Explain me all steps used?

Hi, I've been doing limit problems, and just got to this problem and I can't solve it. I would love some tips; you don't have to solve my problem. Screenshot by Lightshot

Hi guys, I'm a mathematician from Miami Florida working in paraquaternionic and symplectic differential geometry, but I come from a very extensive physics background, pretty much well-versed in all modern physics. But my favorite of all is probably the philosophy of mathematics and science as...

In this video of Laplace transforms the equation $$\lim_{t \to \infty}\frac{te^{-st}}{-s}$$ is said to be 0. I'm not sure I agree with the reasoning. It says it's because $$e^t$$ grows faster than $$t$$; can you treat infinity like that? For example could you say $$\lim_{x \to...

okay...if you accept that the sequence 1+2+3+4...=-1/12, I think I have determined a finite value of infinity. To find the value of the sums of all natural numbers up to a number, you can use the equation ((x^2)+x)/2. An example would be 4. 4+3+2+1=10. ((4^2)+4)/2 also equals 10. following...

Homework Statement How to use Taylor series for condition x>>1? For example f(x)=x\sqrt{1+x^2}(2x^2/3-1)+\ln{(x+\sqrt{1+x^2})} Homework EquationsThe Attempt at a Solution I try to derived it and limit to infinity...for example first term \frac{x^4}{3\sqrt{1+x^2}}. Limit this to infinity is...

Homework Statement http://www5b.wolframalpha.com/Calculate/MSP/MSP19531i2efadg8b4hce2f00000hb7532fcd20a6h7?MSPStoreType=image/gif&s=47&w=253.&h=47. basically I have to evaluate the limit on LHS , the above image is from wolfram alpha . (if link doesn't work , it's limit of...

If I toss a single, composite particle toward a gravitational singularity, would the quarks inside it be tidally rip apart from their confinement with enough energy to create another pair of quarks? And if so, how many times can that process happen before space gets small enough so that...

Homework Statement http://puu.sh/cKVxE/fb13f83a75.png In this image, I have no idea what the math behind this problem is. What exactly is happening here? Homework Equations The Attempt at a Solution I multiplied n/10 in order to get 10000n^9 as a denominator but the ln(2) confuses me...

So this goes to 0. Is this because e^(-x) going to infinity is = to 0 and thus both parts of this equation is equal to 0 ? If so, is there anyway I can prove this through my work? Thank you.

For each series, decide whether they converge or not: k≥1∑2/(k(k+2)) So, I am trying to use the Integral test on this problem. After applying partial fractions I receive the answer of ln(x)-ln(x+2) from 1 to infinity. Evaluating 1 is pretty straight forward.. ln(3). Which seems to be the...

Homework Statement I am having trouble integrating ∫ (x = -∞ to +∞) x3e-αx2 dx part--is this 0 or 1/α2? And, could someone explain? I am pretty sure that, when ∫ (x =0 to +∞) x3e-αx2 dx = 1/α2 However, with x = -∞ to +∞, and the function of the equation being odd, I am lost.Homework Equations...

Need help on exercise 2 from the linked image , left first in so you guys could see the Γ(χ) function any help is appreciated , thanks in advance!

I seem to recall reading a geometry method that showed zero to be the inverse of infinity. Can you give me a reference for that?

lim x-> -(infinity) = x + sqrt(x^2 + 2x) I know that you're supposed to multiply and divide it by it's conjugate and that the answer is -1. But I don't understand how the denominator x - sqrt(x^2 + 2x) = x + x*sqrt[1+(2/x^2)] = x[1+sqrt(1+(2/x^2)].

I have this problem $$\lim_{{x}\to{\infty}} \frac{2x + 1}{ \sqrt{x^2 + 2x + 1} + x}$$ How do I get from there to this step? $$\lim_{{x}\to{\infty}} \frac{2x}{ \sqrt{x^2 } + x}$$ From the last step I can calculate them limit as 1.

After some integration, i am getting a form e^{i \alpha\phi+i\beta\phi\sin(\phi-\phi')-i\gamma\sin\phi} , where ##\alpha, \beta, \gamma## are constants. Now i want to apply the limit where ##\phi ## ranges from 0 to ##\infty ## (ya, in the argument of sine we will encounter ##\infty ## which is...

I understand the derivation of gravitational potential energy when an object is moved away from Earth but when I try to derive the formula for gpe by considering a test mass moving from infinity to r then I end up with a positive gravitational potential energy. Because integrating F.dr from...

Homework Statement I am trying to grasp infinity. Homework Equations Please tell me which are false and which are true (the statements). If false explain why, don't just say because so and so said so, please EXPLAIN the concept otherwise I will never learn or explain the true...

For example; Please tell me which are false and true. If false explain why, don't just say because so and so said so, please EXPLAIN the concept otherwise I will never learn or explain the true answer! Can infinity odd or even? If not what state is it in? Or the fact that it is never...

Is there a way to distinguish between rational functions that have the same limit at both ends and those that don't? I think I might have answered my own question, but let's say I evaluate a rational function, and it turns out to be a coefficient ratio with no variables (3/2). Does that mean...

If the bulk universe is infinite (IF it is), would mathematical physics have trouble describing it because infinity is not a number?

I'm working through some problems from Stewart's Calulus, 6ed. and am having some difficulty with certain limit proofs. In particular, there is no definition provided for limits of the form: $$ \lim_{x \to - \infty} f(x) = L $$ One of the exercises is to come up with a formal definition...

A phrase that I heard several times in the 2 years of high school AP physics I've completed (being a computer science major, I haven't taken any physics classes in college) was moving an object from "infinity to a point" and I'm a little confused as to what that means and how it works. Also...

1. $$=\lim_{{x}\to{\infty}} (x^3+\sqrt{x^6+x^3+1}$$ Multiplying top and bottom by $$x^3-\sqrt{x^6+x^3+1}$$, we get: $$=\lim_{{x}\to{\infty}} \frac{x^3+1}{x^3-\sqrt{x^6+x^3+1}}$$ Dividing by the highest power: $$=\lim_{{x}\to{\infty}} \frac{1+\frac{1}{x^3}}{1-\sqrt{1+\frac{1}{x^3}}}$$...

Is infinity part of any set?

We know that the derivative of the general Schwartz - Christoffel map (function) is: f'(z) = λ(z - x_1)^{a_1}...(z-x_n)^{a_n} Question: In various sources around the web, it is mentioned that x_n can be taken to be the "point at infinity", and the last factor can be removed from the above...

Express $\displaystyle \sum_{n=1}^{\infty}\sum_{m=1}^{\infty} \dfrac{1}{m^2n+mn^2+2mn}$ as a rational number.

If our universe has a history of infinity of cause-effects/time, how could it ever traverse that infinity to reach 'now'. I mean to say, even if our universe started with a big bang, there must have been some cause for it, then a cause for the cause that caused big bang and so on ad...

Went to a tutor for help with this problem and he was stumped need to find the limit 2 - t + sin t/ t + cos t book says answer is -1 My attempts I tried two things 1. I just substituted 0 2-0 + sin(0)/ 0 + cos(0) 2/1 2 wrong answer 2. I divided everything by the...

calculate the Fourier transform of the function g(x) if g(x) = 0 for x<0 and g(x) = ##e^{-x}## otherwise. putting g(x) into the transform we have: ##\tilde{g}(p) \propto \int_{0}^{inf} e^{-ipx} e^{-x} dx## which we can write: ##\tilde{g}(p) \propto \int_{0}^{inf} e^{-x(ip+1)} dx##...

Homework Statement This may not be the correct place to ask but the problem gives a graph of f'(x)=e^-x^2 with a particular solution f(0)=0. It then asks you to find the limit of f(x) as it approaches infinity using a graphing calculator options .886 .987 1.0 1.414 inf Homework...

Is correct to state that: ##x \infty = \text{sgn}(x) \infty## ##\infty^x = \infty^{\text{sgn}(x)}## ?

A little confused here.. what does $$\frac{(2n-1)!}{2n!}$$ as n---> $$\infty$$ = to? How would I look at that by inspection and figure it out because I am confused.. isn't 2! = 1 * 2 and 3! = 1 * 2 * 3? but what is 2n! factorial... Also What is 2n-1! factorial equal to

Homework Statement If I have a wave function that goes to infinity can I assume that the derivative also goes to 0 at infinity? Homework Equations The Attempt at a Solution The reason I think it does is because the wavefunction and its derivative must be continuous everywhere...

Can someone check my solutions? Do the following sequences $${a_n}$$ converges or diverge as$$ \n\to\infty$$? If a sequence converges find its limit. Justify your answers. 1. $$a_n = 2 +(-1)^n$$ Answer: so can I say that as lim n --> infinity the sequence diverges by oscillation? 2. $$a_n =...

Homework Statement I have been trying solve this ask, but there is a problem. I don´t know how I can obtain an expression of infinity which is connected with angle. Picture is as Attach Files2. The attempt at a solution I think, I must use this equations AAB=m * ∫ * K dr = Δ Ek Is there...

Force can be expressed as F = P/v where P = power (watts) and v = velocity (metres per second) So what happens when you use a given amount of power to accelerate an object from rest? This would be given by: a = P/(mv) And since v = 0 => a = P/(m*0) This would be division by 0...

Hello, this isn't a homework problem, so I'm hoping it's okay to post here. I would like to know the correct way to mathematically express the idea in my title. It is intuitively obvious that as the radius of a circle increases, it's curvature decreases. I looked it up and found that...

Relevant Information A language is a set of strings over an alphabet A string is a finite set of characters from an alphabet An alphabet is a finite non-empty set A DFA is a deterministic finite state machine A subset of it's states are accept states A string is accepted by a DFA if the...

Homework Statement Consider the infinite region in the first quadrant between the curve y=e^-5x and the x-axis. Find area= 1/5 (got this part) Compute the volume of the solid generated by revolving the region about the x-axis: Compute the volume of the solid generated by revolving the...

Homework Statement Prove that if f(z) is analytic at infinity, then it has expansion of the form f(z) = \sum_{n=0}^{+\infty} \frac{a_{n}}{z^{n}} converging outside some disk.2. The attempt at a solution I know that for f(z) to be analytic at infinity we want to consider the composite...

For the following algebraic expressions for the Laplace transform of a signal, determine the number of zeros located in the finite \(s-\)plane and the number of zeros located at infinity. Does that mean pole since at a pole the plot will diverge to \(\infty\)? Otherwise, what would be a zero...

Evaluate $\dfrac{1}{3^2+1}+\dfrac{1}{4^2+2}+\dfrac{1}{5^2+3}+\cdots$

Okay, let's say you have an infinitely long line segment. Using area and volume formulas for different shapes, would you get an infinitely large shape that the formula was for in the first place? Area: For rectangles, would you get an infinitely large rectangle with A = l * w? What about...

Why is gravitational potential energy defined at infinity? Like here on Earth there is Zero potential energy at the center of the Earth (if you could theoroeetically go there) so why not define it as 0 at zero distance from the force supplier instead of at infinity? I understand why the...

hey pf! can someone shed some light on why odd integrals don't necessarily converge over infinite symmetric domains? thanks!

Homework Statement 180\int_5^\propto \frac{2}{(4+x^{2})^{3/2}} dx Homework Equations Trigonometric Substitutions: (x=2 tan z). The Attempt at a Solution I've computed the integral and ended up with 180 [\frac{x}{2(4+x^2)^{1/2}}] from 5 to infinity. I could've easily computed...