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set
Recent questions tagged set
29
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1
answers
Define an open set in a metric space.
Define an open set in a metric space.
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Apr 8
Mathematics
define
open
set
metric
space
+
–
116
views
1
answers
Given a sequence ${\{x_n\}_{n\in\mathbb{N}}}$ in a metric space X, prove the following statements:
Given a sequence ${\{x_n\}_{n\in\mathbb{N}}}$ in a metric space X, prove the following statements:(a) If $d(x_n,x_{n+1}) < 2^{-n}$ for every $n \in \mathbb{N}$, then ${\{...
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113k
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Mar 11
Mathematics
set
function
convex
closed
nonempty
compact
interior
+
–
77
views
1
answers
Prove that $f_n$ converges uniformly on compact subsets of $\Omega$.
Let $\Omega$ be a region, and $f_n \in \mathcal{H}(\Omega)$ for all $n$. Set $u_n = \Re(f_n)$, and suppose $u_n$ converges uniformly on compact subsets of $\Omega$ and th...
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113k
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Mathematics
prove
set
function
sequence
bounded
converge
open
+
–
93
views
1
answers
If $A, B$ are disjoint subsets of the plane, $A$ is compact, $B$ is closed, then there exists a $\delta > 0$ such that, . . .
if $A, B$ are disjoint subsets of the plane, $A$ is compact, $B$ is closed, then there exists a $\delta 0$ such that, for all $\alpha \in A$, $\beta \in B$, $| \alpha - ...
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113k
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Mar 10
Mathematics
set
open
metric
spaces
vectors
scalars
components
+
–
143
views
1
answers
Let $\{ x_i \}_{i=1}^n \subset \mathbb{R}^D$ be a discrete set on unique points.
Let $\{ x_i \}_{i=1}^n \subset \mathbb{R}^D$ be a discrete set on unique points. Recall that the DBSCAN algorithm depends on two parameters: $\epsilon$ and MinPts.(a) Des...
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113k
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Mar 10
Mathematics
numbers
distinct
palindromic
natural
primes
vector
set
+
–
100
views
1
answers
Suppose $x_1,...,x_n \in \mathbb{R}^D$ are data points, and we introduce an outlier $x^o$ with the property that . . .
Suppose $x_1,...,x_n \in \mathbb{R}^D$ are data points, and we introduce an outlier $x^o$ with the property that, for some $\delta 0$, $\Vert x_i - x^o \Vert_2 \delta$...
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Mar 10
Mathematics
set
real
function
vector
convex
open
convexity
+
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72
views
1
answers
Let $x_1,...,x_n \in \mathbb{R}^d$. Fix some positive integer $K$.
Let $x_1,...,x_n \in \mathbb{R}^d$. Fix some positive integer $K$. Let $C_1,...,C_K$ be a partition of the data with centroids $\mu_1,...,\mu_K$. Let$$ F(C_1,...,C_k) \s...
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Mathematics
real
set
function
vector
convex
open
convexity
+
–
66
views
1
answers
When dimension reducing data in $\mathbb{R}^D$ using PCA, the choice of embedding dimension is crucial.
When dimension reducing data in $\mathbb{R}^D$ using PCA, the choice of embedding dimension is crucial. Many heuristics exist to estimate a good dimension. One is to choo...
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113k
points
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Mar 10
Mathematics
real
set
equation
analysis
line
epsilon
theory
+
–
65
views
1
answers
Recall that the variance of a set of numbers $x_1,...,x_n \in \mathbb{R}$ is defined as
Recall that the variance of a set of numbers $x_1,...,x_n \in \mathbb{R}$ is defined as $\sigma^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2$, where we define the mean as $...
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Mar 10
Mathematics
function
set
vector
real
convex
open
convexity
+
–
99
views
1
answers
Solution \( e^{i \pi}+1=0 \)
Solution \( e^{i \pi}+1=0 \)
S.A9
114
points
S.A9
asked
Feb 24
Mathematics
equation
prove
sequence
function
set
euler
+
–
94
views
1
answers
Explain \( e^{i \pi}+1=0 \)
Explain \( e^{i \pi}+1=0 \)
S.A9
114
points
S.A9
asked
Feb 24
Mathematics
equation
prove
sequence
euler
function
beautiful
set
+
–
168
views
1
answers
Can I perform multiple hypothesis tests on the same data set?
Can I perform multiple hypothesis tests on the same data set?
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113k
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Feb 17
Research Design
perform
multiple
hypothesis
tests
data
set
+
–
118
views
1
answers
If \( 2^{m+n}=32 \) and \( 3^{3 m-2 n}=243 \) find \( m: n= \) ?
if \( 2^{m+n}=32 \) and \( 3^{3 m-2 n}=243 \) find \( m: n= \) ?
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113k
points
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Feb 17
Mathematics
function
set
real
equation
positive
calculate
solution
+
–
70
views
1
answers
Let \( \left\{f_{i}\right\} \) be a uniform Cauchy sequence consisting of uniformly continuous functions on a closed, bounded interval \( I \). Show that the limit is uniformly continuous.
Let \( \left\{f_{i}\right\} \) be a uniform Cauchy sequence consisting of uniformly continuous functions on a closed, bounded interval \( I \). Show that the limit is uni...
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113k
points
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Feb 16
Mathematics
sequence
cauchy
triangle
inequality
set
prove
converge
+
–
129
views
1
answers
Show that for any \( 0<a<1 \) the sequence \( \left\{x^{i}\right\} \) converges uniformly to 0 on \( [0, a] \), but not for \( a=1 \).
Show that for any \( 0<a<1 \) the sequence \( \left\{x^{i}\right\} \) converges uniformly to 0 on \( [0, a] \), but not for \( a=1 \).
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113k
points
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Feb 16
Mathematics
prove
converge
uniformly
sequence
set
construct
sequences
+
–
86
views
1
answers
How do I test whether the function \(y=x^2-3x+12\) is continuous from the left and from the right and to identify any discontinuities
How do I test whether the function \(y=x^2-3x+12\) is continuous from the left and from the right and to identify any discontinuities
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113k
points
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asked
Feb 15
Mathematics
function
continuous
integers
set
domain
establish
real
+
–
99
views
1
answers
Normalize the set of functions \( \phi_{n}(\theta)=e^{i n \theta} \), \( 0 \leq \theta \leq 2 \pi \). To do so, you need to multiply the functions by a so-called normalization constant \( N \) so that the integral \( N N^{*} \int_{0}^{2 \pi} \phi_{m}^{*}(\theta) \phi_{n}(\theta) d \theta=1 \) for \( m=n \).
Normalize the set of functions \( \phi_{n}(\theta)=e^{i n \theta} \), \( 0 \leq \theta \leq 2 \pi \). To do so, you need to multiply the functions by a so-called normaliz...
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113k
points
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Feb 6
Mathematics
set
open
function
real
convex
convexity
+
–
597
views
2
answers
Prove that \(n^2=(n+1)(n-1)+1\)
Prove that \(n^2=(n+1)(n-1)+1\)
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113k
points
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asked
Jun 14, 2023
Mathematics
prove
real
function
sequence
set
vector
convexity
+
–
167
views
1
answers
(Lael and Nourouzi 2008) Let \((V, \mu, \nu)\) be an \(I F\)-normed space. Assume further that \(\mu(x, t)>0\) for all \(t>0\) implies \(x=0\).
(Lael and Nourouzi 2008) Let \((V, \mu, \nu)\) be an \(I F\)-normed space. Assume further that \(\mu(x, t)>0\) for all \(t>0\) implies \(x=0\). Define\[\|x\|_\alpha=\inf ...
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113k
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asked
May 21, 2023
Mathematics
real
set
complex
jee
numbers
associative
law
+
–
517
views
1
answers
Prove that \(x^2+2 x y+2 y^2\) cannot be negative for \(x, y \in \mathrm{R}\).
Prove that \(x^2+2 x y+2 y^2\) cannot be negative for \(x, y \in \mathrm{R}\).
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113k
points
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May 14, 2023
Mathematics
calculus
proof
algebra
real-numbers
prove
function
set
+
–
387
views
1
answers
What is a non-central t-distribution?
What is a non-central t-distribution?
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Bronze Status
9.4k
points
Maths-Genie
asked
Mar 14, 2023
AI & Data Science
non-central
t-distribution
set
+
–
322
views
1
answers
Why is pi important in mathematics?
Why is pi important in mathematics?
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Bronze Status
9.4k
points
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asked
Mar 13, 2023
Mathematics
important
mathematics
codomain
study
basic
available
set
+
–
548
views
2
answers
Define an uncountable set
Define an uncountable set
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9.4k
points
Maths-Genie
asked
Mar 7, 2023
Mathematics
define
uncountable
set
countable
subset
+
–
380
views
2
answers
What is an unbounded set?
What is an unbounded set?
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Bronze Status
9.4k
points
Maths-Genie
asked
Mar 7, 2023
Mathematics
unbounded
set
range
function
domain
+
–
515
views
1
answers
Which sets of numbers are part of the set of real numbers?
Which sets of numbers are part of the set of real numbers?
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Platinum
113k
points
MathsGee
asked
Feb 14, 2023
Mathematics
real
set
numbers
function
sets
natural
structures
+
–
260
views
1
answers
Can mathematics teaching be seen as a messy set of functions?
Can mathematics teaching be seen as a messy set of functions?
AstraNova
Diamond
68.1k
points
AstraNova
asked
Feb 6, 2023
Mathematics
mathematics
teaching
messy
set
functions
+
–
605
views
1
answers
What structures does the set of real numbers carry?
What structures does the set of real numbers carry?
AstraNova
Diamond
68.1k
points
AstraNova
asked
Feb 2, 2023
Mathematics
structures
set
real
numbers
carry
+
–
315
views
1
answers
What is set theory?
What is set theory?
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Diamond
68.1k
points
AstraNova
asked
Feb 2, 2023
Mathematics
theory
set
axiom
important
basic
study
available
+
–
479
views
1
answers
How are equivalence relations used in mathematics?
How are equivalence relations used in mathematics?
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Diamond
68.1k
points
AstraNova
asked
Feb 2, 2023
Mathematics
relations
equivalence
set
theory
classes
jee
union
+
–
303
views
1
answers
What is the cardinality of the set of real numbers?
What is the cardinality of the set of real numbers?
AstraNova
Diamond
68.1k
points
AstraNova
asked
Feb 2, 2023
Mathematics
cardinality
set
real
numbers
natural
+
–
538
views
1
answers
What is the cardinality of the set of natural numbers?
What is the cardinality of the set of natural numbers?
AstraNova
Diamond
68.1k
points
AstraNova
asked
Feb 2, 2023
Mathematics
cardinality
set
natural
numbers
+
–
527
views
1
answers
In the figure below, DC is the diameter of a circle with centre O. CE is a tangent to the circle at \(C\). The diagonals of cyclic quadrilateral \(A B C D\) intersect at \(F\).
In the figure below, DC is the diameter of a circle with centre O. CE is a tangent to the circle at \(C\). The diagonals of cyclic quadrilateral \(A B C D\) intersect at ...
AstraNova
Diamond
68.1k
points
AstraNova
asked
Jan 30, 2023
Mathematics
product
vector
set
space
eigenspace
fields
closed
+
–
467
views
1
answers
Prove that the polynomial \(x^5 - x^4 + x^3 - x^2 + x - 1\) is reducible over the integers.
Prove that the polynomial \(x^5 - x^4 + x^3 - x^2 + x - 1\) is reducible over the integers.
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Diamond
68.1k
points
AstraNova
asked
Jan 27, 2023
Mathematics
function
real
set
vector
convex
open
convexity
+
–
200
views
0
answers
Prove these trig expressions
Prove the following:(a) \((\cos \theta+\sin \theta)^2=1+\sin 2 \theta\)(b) \(\frac{\cos 2 x}{\cos x-\sin x}=\cos x+\sin x\)(c) \(\cos ^4 \alpha-\sin ^4 \alpha=\cos 2 \alp...
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Diamond
68.1k
points
AstraNova
asked
Jan 24, 2023
Mathematics
prove
identity
trigonometric
sine
cosine
set
expression
+
–
217
views
1
answers
Evaluate \(\sum_{k=0}^8 2 k=\)
Evaluate \(\sum_{k=0}^8 2 k=\)
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Platinum
113k
points
MathsGee
asked
Jan 21, 2023
Mathematics
function
series
real
set
vector
convex
open
+
–
398
views
0
answers
Prove that the function $f(x) = \frac{1}{x}$ is uniformly continuous on the interval $(1,\infty)$.
Prove that the function $f(x) = \frac{1}{x}$ is uniformly continuous on the interval $(1,\infty)$.
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113k
points
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asked
Jan 10, 2023
Mathematics
prove
uniformly
interval
function
continuous
converge
set
+
–
544
views
0
answers
Prove that if $(x_n)$ is a sequence of points in a metric space $(X,d)$, then $(x_n)$ has a convergent subsequence if and only if it is a Cauchy sequence.
Prove that if $(x_n)$ is a sequence of points in a metric space $(X,d)$, then $(x_n)$ has a convergent subsequence if and only if it is a Cauchy sequence.
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Platinum
113k
points
MathsGee
asked
Jan 10, 2023
Mathematics
function
set
convex
nonempty
closed
compact
interior
+
–
331
views
1
answers
How important are aesthetics in mathematics?
How important are aesthetics in mathematics?
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Platinum
113k
points
MathsGee
asked
Dec 29, 2022
Mathematics
mathematics
important
study
available
basic
set
theory
+
–
267
views
1
answers
The model developed from sample data that has the form of \(\hat{y}=b_0+b_1 x\) is known as
The model developed from sample data that has the form of \(\hat{y}=b_0+b_1 x\) is known asa. regression equationb. correlation equationc. estimated regression equationd....
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113k
points
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asked
Dec 24, 2022
AI & Data Science
equation
model
regression
estimated
function
set
vector
+
–
579
views
0
answers
Define a function \(f\) on the unit interval \(0 \leq x \leq 1\) by the rule
Define a function \(f\) on the unit interval \(0 \leq x \leq 1\) by the rule\[f(x)= \begin{cases}1-3 x & \text { if } 0 \leq x<1 / 3 \\ 3 x-1 & \text { if } 1 / 3 \leq x<...
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Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
function
vector
set
real
open
convex
convexity
+
–
501
views
0
answers
Let \(A B C D E F\) be a regular hexagon. Let \(P\) be the intersection point of \(\overline{A C}\) and \(\overline{B D}\). Suppose that the area of triangle \(E F P\) is 25 . What is the area of the hexagon?
Let \(A B C D E F\) be a regular hexagon. Let \(P\) be the intersection point of \(\overline{A C}\) and \(\overline{B D}\). Suppose that the area of triangle \(E F P\) is...
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Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
product
point
set
vector
space
prove
hexagon
+
–
342
views
0
answers
If \(x\) is a real number such that \((x-3)(x-1)(x+1)(x+3)+16=116^2\), what is the largest possible value of \(x\) ?
If \(x\) is a real number such that \((x-3)(x-1)(x+1)(x+3)+16=116^2\), what is the largest possible value of \(x\) ?
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Platinum
113k
points
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asked
Dec 8, 2022
Mathematics
real
numbers
jee
set
integers
complex
associative
+
–
294
views
0
answers
Let \(T\) be the convex hull of the two current triangles. What is the volume of \(T\) ?
Let \(P\) be a right prism whose two bases are equilateral triangles with side length 2. The height of \(P\) is \(2 \sqrt{3}\). Let \(l\) be the line connecting the centr...
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Platinum
113k
points
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asked
Dec 8, 2022
Mathematics
set
vector
space
product
closed
eigenspace
fields
+
–
389
views
0
answers
How many quadratics are there with these properties?
Mr. Jones teaches algebra. He has a whiteboard with a pre-drawn coordinate grid that runs from \(-10\) to 10 in both the \(x\) and \(y\) coordinates. Consequently, when h...
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Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
numbers
combinations
permutations
set
integers
real
complex
+
–
424
views
0
answers
There are 300 points in space. Four planes \(A, B, C\), and \(D\) each have the property that they split the 300 points into two equal sets. (No plane contains one of the 300 points.)
There are 300 points in space. Four planes \(A, B, C\), and \(D\) each have the property that they split the 300 points into two equal sets. (No plane contains one of the...
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
product
vector
set
space
circle
trapezoid
inscribed
+
–
365
views
0
answers
How many cool sequences are there?
Say that a sequence \(a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8\) is cool if- the sequence contains each of the integers 1 through 8 exactly once, and- every pair of consecu...
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113k
points
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asked
Dec 8, 2022
Mathematics
combinations
permutations
numbers
integers
set
real
complex
+
–
401
views
0
answers
Let \(H\) be a regular hexagon with area 360 . Three distinct vertices \(X, Y\), and \(Z\) are picked randomly, with all possible triples of distinct vertices equally likely. Let \(A, B\), and \(C\) be the unpicked vertices.
Let \(H\) be a regular hexagon with area 360 . Three distinct vertices \(X, Y\), and \(Z\) are picked randomly, with all possible triples of distinct vertices equally lik...
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
real
numbers
set
jee
integers
complex
associative
+
–
326
views
0
answers
Let \(m\) and \(n\) be positive integers such that \(m^4-n^4=3439\). What is the value of \(m n\) ?
Let \(m\) and \(n\) be positive integers such that \(m^4-n^4=3439\). What is the value of \(m n\) ?
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
positive
function
real
prove
set
open
vector
+
–
229
views
0
answers
Let \(a_n=n(2 n+1)\). Evaluate \[ \left|\sum_{1 \leq j<k \leq 36} \sin \left(\frac{\pi}{6}\left(a_k-a_j\right)\right)\right| . \]
Let \(a_n=n(2 n+1)\). Evaluate\[\left|\sum_{1 \leq j<k \leq 36} \sin \left(\frac{\pi}{6}\left(a_k-a_j\right)\right)\right| .\]
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Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
function
real
set
vector
convex
open
convexity
+
–
274
views
0
answers
Let \(O\) be the set of odd numbers between 0 and 100 . Let \(T\) be the set of subsets of \(O\) of size 25 . For any finite subset of integers \(S\), let \(P(S)\) be the product of the elements of \(S\).
Let \(O\) be the set of odd numbers between 0 and 100 . Let \(T\) be the set of subsets of \(O\) of size 25 . For any finite subset of integers \(S\), let \(P(S)\) be the...
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
convex
convexity
set
vector
real
function
open
+
–
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