1. ### B My argument why Hilbert's Hotel is not a veridical Paradox

Hello there, I had another similar post, where asking for proof for Hilbert’s Hotel. After rethinking this topic, I want to show you a new example. It tries to show why that the sentence, every guest moves into the next room, hides the fact, that we don’t understand what will happen in this...
2. ### B Hilbert's Hotel: new Guest arrives (Infinite number of Guests)

Hilberts Hotel has infinity numbers of rooms and in every room is exactly one guest. On Wikipedia Hilberts Hotel gets described as well: Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest...
3. ### Find the range of y in a DE

From integration by parts, and using y(10) = 0, I get the equation ##2e^{3t-30} = \frac{|y-2|}{|y+1|}.## Let ##f(t) = 2e^{3t-30}##. Since it's for t>10, f(10) = 2, and we have ##2=\frac{|y-2|}{|y+1|}##. Depending on the sign I choose to use, I get either that y=-4 or y =0. Since ##t: 10...
4. ### I Completed infinity

If actual infinity represents a completed set of infinite data points, wouldn't that be a contradiction of terms?
5. ### I Why is the Laplace transform unchanged when t is replaced with -t?

In Mathematical Methods in the Physical Sciences by Mary Boas, the author defines the Laplace transform as... $${L(f)=}\int_0^\infty{f(t)}e^{-pt}{dt=F(p)}$$ The author then states that "...since we integrate from 0 to ##\infty##, ##{L(f)}## is the same no matter how ##{f(t)}## is defined for...
6. ### B Could singularities be just rips in the space-time fabric?

First off, this is just an assumption. My knowledge of the field is extremely limited and I beg you to come and correct my mistakes, so I can learn. So, I guess we all know how that space-time fabric is bended by gravity. When a star dies, all of the atoms are brought extremely close...
7. ### B Does undefined always mean infinity?

While using L' Hospital's rule in evaluating limits, one comes across limits of the following type: $$\lim_{x \to 0} x \ln x$$ Such limits are generally evaluated by taking ##x## to the denominator and make it ##x^{-1}##. In such a case, an indeterminate form ##\frac{\infty}{\infty}## comes...
8. ### B Is infinity truly infinite if it has something else in it?

Is infinity truly infinite if it has something else in it? Put differently, say there's an infinite volume of water that has some rocks in it, is the volume of water truly infinite? Though there's a place where there's no water?
9. ### A How is Inaccessible Cardinal Written?

I'm writing some notes on set theory, Aleph Null, etc., and was wondering if there's a Notation or Symbol that abbreviates this (inaccessible/strong/uncountable etc. cardinals). I'm not sure if ive seen notation before but it seems like symbols resembling Theta and phi have been used.
10. ### Insights Intro to Big Bang and Infinity Concepts - Comments

Greg Bernhardt submitted a new PF Insights post Intro to Big Bang and Infinity Concepts Continue reading the Original PF Insights Post.
11. ### I Where has this proof gone wrong? ∞= 1/0

Now I expect that most of you on this forum would be familiar with the equality between point nine reoccurring and one: 0.999...=1 If your not familiar please review https://en.wikipedia.org/wiki/0.999... Now this equality can be used to imply something else, which is rather heterodox...
12. ### I Infinite versus finite space

I have read some of the other posts about this topic but am still left unsatisfied. Could just be me. :cool: Did the universe, one minute after the big bang, consist of a finite volume of spacetime? If so, then is it not logically inconsistent that the universe can possibly be infinite now...
13. ### Lim x->0+ (x^cos(1/x))

Homework Statement Homework Equations The Attempt at a Solution let y = lim x->0+ x^cos(1/x) lny = cos(1/x)*lnx = (x*cos(1/x)) * (lnx/x) x*cos(1/x) = 0 (sandwich theorem) lnx/x = 0 (l'hopital) so lny = 0 and y = 1 Is this correct?
14. ### Find the limit of the expression

Homework Statement $$\lim_{x\to\infty} \left(\frac{n^2+2n+1}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}$$ Homework Equations 3. The Attempt at a Solution [/B] I tried ##\lim_{x\to\infty} \left(\frac{n^2+2n+3-2}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}=## ##\lim_{x\to\infty}...
15. ### I Where do we use infinity in physics, and why?

Hello! I'm doing a school project, where I am writing about Infinity in Math and Physics. I've got the math part settled, but it's the physics part that has begun to bother me. One part of my task is to write about some of the mathematical expressions in physics, where we use infinity - but the...
16. ### B What are surreal numbers?

Hey guys! I have heard of this concept in various places and sort of understands what it attempts to do. Can anybody please explain it to me in more detail like how it works, how to notate it, and how to expand it to infinities and infinitesimals. Thanks in advance! Aakash Lakshmanan xphysx.com...
17. ### B What percentage of the universe do we know

Hello. First of all, I must say that I'm new to this forum, so I apologize if I'm posting in the wrong section. I'm a 17 year old with not that much knowledge about physics, so if what I'm talking about makes no sense or is completely stupid, just let me know. A couple of days ago I asked...
18. ### Inifinity limit with natural log

Homework Statement Limx--> ∞ Ln(x^2-1) -Ln(2x^2+3) Homework Equations The Attempt at a Solution Ln(x^2-1)/(2x^2+3) Then I divided the top and bottom by x^2 so in the end I got (1/2). Is this right?
19. ### Limit at infinity with radicals

Homework Statement lim as x tends to -∞ (x)^3/5 - (x)^1/5 Homework Equations The Attempt at a Solution The first thing I did was convert it into a radical so it becomes fifthroot√x^3 - fifthroot√x. Then I rationalized to get ( x^3-x)/(fifthrt√x^3+fifthroot√x) . I then divided the top by...
20. ### B Can the space (or else measurable) be actually infinite?

The (most popular) flat model of Universe is space-infinite. How the infinity is measured? Can you give me references to the papers about the actual infinity of space?
21. ### I When observable Universe was the size of a baseball was its gravitational influence bigger?

When the observable universe was the size of a baseball, did its gravity (field?) extend to (as opposed to towards) infinity?
22. ### B Ratio of circumference to diameter for infinitely large circ

If you divided the circumference of an infinitely large circle by its diameter, would the result be pi?
23. ### B Why do we use infinity in Physics?

When we talk about a particular problem in Physics. For instance, let's say that light is coming from somewhere to hit the earth. We often say that the light is coming from "infinity." Let's say that we're tackling a black hole and we have a person somewhere as an example and we say that let's...
24. ### Infinity question - limits

Is ## "\frac{0}{\infty}"=0 ## ?
25. ### B Is the Universe finite?

The universe- from our understanding, is expanding, thus the regions (for lack of a better word) particles have not yet reached do not exist. How far our universe can/ will expand is unknown, it may be infinite, but we can conclude at this time, as it is still expanding, that it is finite. True...
26. ### B Expanding from and eventually to a singularity?

I know this thread, about why the Universe can't expand inward, is fairly old; but I stumbled across it today and there was something mentioned here that sparked a question I feel like people here would be qualified to answer. What was mentioned, was that a singularity is a point at which our...
27. ### A Infinity in the real world?

To what extent is the term infinity used in the physical world. When talking in terms of mathematics we can have a set of all natural numbers called an infinity, then we can have a value that comes after this set of infinity (lets call it 'a'). After 'a' comes 'a+1' then after this set of...
28. ### I Determining the Rate at Which Functions approach Infinity

With basic fractions, the limits of 1/x as x approaches infinity or zero is easily determine: For example, $$\lim_{x\to\infty} \frac{1}{x} = 0$$ $$\lim_{x\to 0} \frac{1}{x} = \infty$$ But, we with a operation like ##\frac{f(x)}{g(x)}##...
29. ### I can't seem to find this limit

Homework Statement Homework Equations The Attempt at a Solution I tried using the rule of multiplying with the "conjugate", for example what's above multiplied by (√n^3+3n)+(√n^3+2n^2+3)/(√n^3+3n)+(√n^3+2n^2+3). But I'm left with a huge mess :( I also tried dividing the top and the bottom...
30. ### What is the electric field due to hollow sphere at R=z?

So I derived the E-field of a hollow sphere with a surface charge σ at z and I got: E(r)=\hat{z}\frac{\sigma R^2}{2\varepsilon _{0}z^2}\left ( \frac{R+z}{\left | R+z \right |}-\frac{R-z}{\left | R-z \right |} \right ) at z>R, the equation becomes: E(r)=\hat{z}\frac{\sigma R^2}{\varepsilon...