Questions tagged [infinity]
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Use this tag for questions on the concept of infinity. Don't use this tag merely because $\infty$ appears somewhere in the question.
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Reflection principle: can any property of a set (model) be reflected?
Can any property of a set be reflected? If no, why? Is there some sort of requirement that must be fulfilled? I've read on the Wikipedia page ,that ... discrete-mathematics set-theory infinity reflection- 21
Preimage of zero under a continuous function on compact real interval has at most countable connected components
As part of a larger inquiry, I suspect and am trying to prove the following : Let $\phi$ be a continuous function defined on $[0,1]$. Then $\phi^{-1}(0)$ has an at most countable number of connected ... continuity cardinals connectedness infinity- 1,199
Why do we use 2 different types of infinity to define the same infinitesimals?
I read in the book "Calculus with infinitesimals" (Efrain Soto Apolinar) that $dx=1/N$ and $N$ is the number of elements of the set of the natural numbers (letter $N$ is used to indicate the ... calculus infinity infinitesimals- 57
Probably silly question on notation
I just wanted to ask, since $\infty$ is not a number, if $\lim_{x \to a}f(x) \to \infty$ and also $\lim_{x \to b}f(x) \to \infty$, can we write $\lim_{x \to a}f(x)$= $\lim_{x \to b}f(x)$? limits notation soft-question infinity- 730
Projecting Skolem's Paradox Upwards
My understanding of the resolution of Skolem's Paradox is that although in a countable model of ZFC there does not exist a bijection between a countable set and its powerset, we can still construct a ... elementary-set-theory model-theory diagonalization infinity- 659
Where is my mistake in evaluating $\lim_{x \to -\infty} \frac{\sqrt{x^2+4}}{x}$?
Given is $\lim_{x \to -\infty} \dfrac{\sqrt{x^2+4}}{x}$ I divide numerator and denominator by x to the largest degree in the denominator and I get $$\lim_{x \to -\infty} \frac{\sqrt{1+\frac{4}{x^2}}}{... calculus limits infinity- 23
Intuitionistic Disproof of Intermediate Value Theorem
For uni I'm studying intuitionism, and I came across the following disproof for the IVT: The thing I'm trying to understand is why this disproof is not valid in classical mathematics. In my research ... real-analysis cauchy-sequences infinity constructive-mathematics- 129
How should one think of infinity. [closed]
I am currently taking a first year course in mathematics and have become a bit confused when confronted with "infinity". We are covering logic and sets and I had the following homework ... elementary-set-theory logic infinity quantifiers- 37
How are H-infinity norm and L-1 norm related?
I have trouble understanding the following expressions which I recently encountered in one paper. Suppose that you have the following transfer function: $G(s) = \frac{E_i(s)}{E_{i-1}(s)}, \quad E_i(s) ... normed-spaces infinity- 1
Dividing by square root of zero equals infinity?
So, my calculator app produced a result that doesn't seem correct to me. According to my calculator, $\frac{1}{\sqrt{0}}=\infty$. By my understanding, $\sqrt{0}=0$ (since $0^2=0$). So, shouldn't $\... fractions infinity- 241
Are there more real numbers in the interval $[1,\infty)$ than in the interval $(0,1]$? Or not?
We all might be familiar with the beautiful method Cantor devised to prove that the cardinality of the set of real numbers is more than that of the set of natural numbers (Refer to: elementary-set-theory solution-verification infinity- 229
Sum of infinitely cut lines
Suppose we split a line which length is $1$ in half. Then we get the $2$ lines which length is $1/2$ . Divide these two lines equally in half. Suppose we repeat this process infinitely. The length of ... infinity- 1
Can we use mathematics and logic to estimate probability of extremely absurd events?
I'd like to detail my question over the example below. Let's say I have a random pixel generator which has $1024 \times 768$ screen resolution. It also has $24$ bit color which means $2^{24}= 16,777,... probability statistics random-variables infinity image-processing- 1
Infinite set such that sum of elements of every finite subset is not a power of $p$
Let $p$, be a prime number, and $S$ an infinite set of positive integers, such that all numbers from $S$ are coprime with $p$. Prove that there is an infinite subset $A\subseteq S$, such that for ... number-theory prime-numbers infinity- 884
Can the continuity be established at $x= 0$ for the function below?
Is this method okay to show that $f(x)=x^{-2/3}$ is discontinuous at point $x= 0$? Limit $f(x)$ as we tends from positive side of $0$, we get $+\infty$ as the value, same with $f(x)$ approached from ... calculus limits continuity infinity- 409
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