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Questions tagged [interval-arithmetic]

Interval arithmetic is the arithmetic of quantities that lie within specified ranges (i.e., intervals) instead of having definite known values.

Interval arithmetic is the arithmetic of quantities that lie within specified ranges (i.e., intervals) instead of having definite known values.

This concept is suitable for a variety of purposes. The most common use is to keep track of and handle rounding errors directly during the calculation and of uncertainties in the knowledge of the exact values of physical and technical parameters. The latter often arise from measurement errors and tolerances for components or due to limits on computational accuracy. Interval arithmetic also helps find reliable and guaranteed solutions to equations and optimization problems.

203 questions
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Why do you get zero by squaring [-1, 1] in interval arithmetic?

In the Wikipedia page on Interval Arithmetic, the example for the Dependency problem is that $f(x) = x^2 + x$ on the interval $\left[-1, 1\right]$ is $\left[-1, 2\right]$. I don't understand why this is the case. Looking at the…
Cedric Martens
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Cartesian Product of Interval

I know what is a cartesian product of sets, for example, $M= \{1,2\} , N = \{a,b\} $ $M \times N = {(1,a), (1,b), (2,a) , (2,b)}$ but what is the Cartesian product of two intervals? say, $[-5,1] \times [-2,3]$
Leonardo
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Why if f(x) = 2x - x on [-1, 1] results in [-1, 2] in Interval Arithmetic?

From the Section 3.1 of this paper The Dependency Problem. The main downside of interval arithmetic is that the computed bounds may be extremely pessimistic. As an example, consider the simple operation ← 2 −, evaluated on the range ∈ [−1, 1].…
Cedric Martens
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Is $[0,\infty )$ a closed interval or a half-closed interval?

Is $[0,\infty)$ a closed interval or a half-closed interval? My confusion is whether infinity is included or not.
Kantura
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Is there a special name given if a number is on the edge of an interval?

For instance, if I have the interval $[0,1]$, is it proper to say that $0$ is on the lower bound of the interval? I'm looking for the most elegant way to express this.
Daniel Scott
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complement of the given interval

A set $M \subseteq \mathbb{R}$ is called open if $\mathbb{R} \setminus M$ is closed. How do you prove that $(2n -1/2, 2n + 1/2)$ is open? I‘m confused because it means $2n - 1/2 < 2n + 1/2$ but how can I write it as a complement? In this case, these…
user1185546
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Let `x` be a real number between two values, let `y` be a real number between two other values. What's the range of `x/y`?

Like the title says: $$ x \in \Bbb R : x \in [x_{min}, x_{max}] $$ $$ y \in \Bbb R : y \in [y_{min}, y_{max}] $$ What is the range of: $$ x \over y $$ ? I find this hard to reason about because the division is discontinuous. I can identify up to 49…
Helloer
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Logic behind addition of two intervals

I would like to know the logic behind adding two intervals $$[a, b]$$ $$[c, d]$$ together and for the sake of simplicity let's say that the numbers in the interval are just integers and not real numbers. I know that the idea is to just add the…
Michael Munta
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What is this interval operation I am doing?

I'm computing the interval C given the intervals A and B that makes the following true: $\forall x_c \in C$ there is a $x_a \in A$ such that $x_a + x_c \in B$. Example: $A = [100,200]$, $B = [300,400]$, $C = [300-200,400-100] = [100,300]$. I was…
Yann
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The percentage of a number within an interval (range of numbers)?

How can I find the percentage of a number in a range of numbers. Let's say the range of numbers are 600-800, so if 600 is 0% and 800 is 100% then how can I find what percentage is 732 in that range of numbers? Thank you in advance.
LiziPizi
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Show that $(a,b)+(c,d) = (a+c,b+d)$

Let $a
Puzzled417
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Evaluating sets and interval union, intersection and exclusion

I am given the sets A = {2,4,6,8}, B = [2,6)andC = (3,8)`. Calculate each of the following. (a) B\A (b) A ∩ B (c) (A ∪ C)\B I think the answer for (b) is {2,4} because B is 2 <= x < 6 and A has the elements 2,4,6,8. so in A and B we are going to…
yowhatsup123
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When given an interval and asked to operate on it do we consider intersection or union?

I had a question: Let $A=[-1,4]$. Find $A^2$ and $\frac{1}{|A|}$. Someone told me that the answers are $A^2=[0,16]$ and $\frac{1}{|A|}=[1,\infty]$. However, if you notice in the first part we are considering a union between $[0,1]$ and $[0,16]$…
This is not me.
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How many evenly spaced steps around unit circle until no gap bigger the Epsillon?

Given a unit circle and a step size, N degrees. How many steps of N degrees until there is no gap between points greater then epsilon deg? Assumptions: yes I know there is logics needed to check for even division into 360, leading to repeat steps. I…
S moran
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Range of a picewise defined function

Let $p(x)$ be defined on $2 \le x \le 10$ such that$$p(x) = \begin{cases} x + 1 &\quad \lfloor x \rfloor\text{ is prime} \\ p(y) + (x + 1 - \lfloor x \rfloor) &\quad \text{otherwise} \end{cases}$$where $y$ is the greatest prime factor of $\lfloor…
Noah D.
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