# Tagged Questions

Use this tag for questions on the concept of infinity. Don't use this tag merely because $\infty$ appears somewhere in the question.

71 views

### Method for computing limit of a sin function as x tends to zero

I have a question about computing $$\lim_{x \to 0} \sin\left(\frac{\pi x}{4|x|}\right)$$ I found the limit of $\pi x$ and $4|x|$ seperately and ended with $\sin(\pi/4)$ which is equal to $1/\sqrt{2}$...
77 views

### Method for computing limit of a function as $x$ tends to zero

I have a question about computing $$\lim_ {x \to 0} \dfrac{(2/x^3)+(1/x^2)+(1/x)+1}{(1/x^3)+1}.$$ I used a shortcut method of dividing by the highest power but I don't think that I can use this method ...
180 views

### May seem like a noob question: really, why can't we divide by 0? [duplicate]

Yes, I know, can't be answered, blah, blah, blah.... but here are a few of my theories. I know, plenty of other questions like this, but before marking this as a duplicate, consider this, my ...
34 views

### One set of functions larger than another set of functions?

This summer I've been slowly working through Halmos's Naive Set Theory. I'm not that far, but I know what lies ahead, which is proving that one infinite set is larger than another (the reals larger ...
3k views

### Can a set be infinite and bounded?

I don't understand a statement in my math book course, I was restudying the compact sets part of the chapter when at a certain moment there is a corollary saying : 'every infinite and bounded part of ...
770 views

### Teaching the Concept of Infinity to Children.

I was recently out with the family and we left it up to the children where we ate lunch (11 and 9 years old). They couldn't agree and were going back and forth calling each other names. This ...
147 views

### Is there a mathematical concept of fractions using transfinite numbers as numerators and denominators?

http://de.wikipedia.org/wiki/Cantors_erstes_Diagonalargument (German) http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument (English) While looking at Cantors method of proof, which he used to ...
295 views

### The nature of infinities

I have been thinking about the nature of infinity lately. I have no experience with higher mathematics or theorems regarding infinity, so please forgive me if my ideas on this topic are extremely ...
86 views

### Deffered annuity with perpetuity

An annuity immediate has $40$ initial quarterly payments of $20$ followed by perpetuity of quarterly payments of $25$ starting in the eleventh year. Find the present value at $4\%$ convertible ...
133 views

### Comparing density of countable infinite sets by examining the association

The two questions that i am asking are in bold. To be clear, i am talking about whole number here. Having seen 3 is everywhere by Numberphile that shows that almost 100% of the whole the numbers ...
68 views

### The limit of $(x^3+\cos x+e^{-2x})/(x^2 \sqrt{x^2+1})$ as $x\to\infty$

I have this infinity problem which I do not know the answer to: $$\lim_{x\to\infty}\frac{x^3+\cos x+e^{-2x}}{x^2 \sqrt{x^2+1}}$$ I thaught that because $x^3$ is the fastest growing part, this would ...
4k views

### Does 0% chance mean impossible? [duplicate]

Suppose we pick a random real number between 0 and 1 and call it $x$. There are $2^{\aleph_0}$ possible values, so the chance of picking any specific number (such as $x$) in that range is 0. But in ...
199 views

### Question about the cardinality of sets and infinity

Let's say we have $\mathbb{N}$, the set of natural numbers: $\{1, 2, 3, 4, 5...\}$ ...which has a cardinality of infinity, and the set $A_x$ which consists of the variable "$x$" (so $\{x\}$). If I ...
85 views

### Is it possible for infinite sets to exist in ZFC with the negation of the Axiom of Infinity? [duplicate]

The Axiom of Infinity states that at least one inductive set exists. Inductive sets are infinite, but not all infinite sets are inductive. Suppose that we take ZFC with the negation of the Axiom of ...
4k views

### Are weird numbers more rare than prime numbers?

By taking a look at the first few weird numbers: $$(70, 836, 4030, 5830, 7192, 7912, 9272, 10430)$$ It is certain that prime numbers occurs more often within this range of numbers. But are weird ...
120 views

120 views

### Assigning values to divergent integrals

I'm interested in the (obviously divergent) integral $$\int_{-\infty}^\infty dx e^{-x f}\ ,$$ where $f$ is real. Is there any way to meaningfully assign a value to this integral? I was thinking of ...
456 views

### What is your intuitive understanding of infinity? [duplicate]

What is your intuitive understanding of infinity? Mine is the following, I prepared it as image: Those were the main points I got to after thinking by myself about what infinity is, without ...
138 views

### $\infty + \infty = \infty$?

(The context is a measure-theoretic one.) I know that $\infty - \infty$ is indeterminate, but what about $\infty + \infty = \infty$? It seems this statement is true and if I input it into Wolfram ...
39 views

### What truly are length, area and volume? And considerations about divergence in normed spaces

All the "(?)" are parts when i'm not sure at all if what i'm saying is right or not, it's just my intuition. Part 1 In $\mathbb{R}$, we can define the length of a segment. In $\mathbb{R}^2$, the '...
153 views

### Is $0$ the midpoint of $(-\infty,+\infty)$?

Is $0$ the midpoint of $(-\infty,+\infty)$? Intuitively, I'd think so, and trying to refine my intuition as to why I'd think so, I would say that this is the case because there is a one-to-one ...
11k views

### How big is infinity?

This might be more philosophy than math, but it’s been bothering me for a while. Question: If there’s an infinite amount of real numbers between $0$ and $1$, shouldn’t there be twice the ...
141 views

### How can I define $\mathbb{N}$ if I postulate existence of a Dedekind-infinite set rather than existence of an inductive set?
Suppose in the axioms of $\sf ZF$ we replaced the Axiom of infinity There exists an inductive set. with the Axiom of Dedekind-infinite set There exists a set equipollent with its proper ...
I tried to prove that $\int\limits_0^\infty t^{x-1} e^{-t} \, \mathrm{d}t$ satisfies the functional equation of the gamma function $\Gamma(x+1)=x\Gamma(x)$, so I partially integrated $\Gamma(x+1)$, ...