Recent questions tagged set

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asked Jun 14 in Mathematics by MathsGee Platinum (98.5k points) | 100 views

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(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 $x=0$.

asked May 21 in Mathematics by MathsGee Platinum (98.5k points) | 76 views

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Prove that $x^2+2 x y+2 y^2$ cannot be negative for $x, y \in \mathrm{R}$.

asked May 14 in Mathematics by MathsGee Platinum (98.5k points) | 165 views

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What is a non-central t-distribution?

asked Mar 14 in Data Science & Statistics by Maths Genie Bronze Status (8.8k points) | 141 views

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Why is pi important in mathematics?

asked Mar 13 in Mathematics by Maths Genie Bronze Status (8.8k points) | 176 views

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Define an uncountable set

asked Mar 7 in Mathematics by Maths Genie Bronze Status (8.8k points) | 169 views

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What is an unbounded set?

asked Mar 7 in Mathematics by Maths Genie Bronze Status (8.8k points) | 187 views

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Which sets of numbers are part of the set of real numbers?

asked Feb 14 in Mathematics by MathsGee Platinum (98.5k points) | 203 views

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Can mathematics teaching be seen as a messy set of functions?

asked Feb 6 in Mathematics by AstraNova Diamond (55.6k points) | 138 views

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What structures does the set of real numbers carry?

asked Feb 2 in Mathematics by AstraNova Diamond (55.6k points) | 162 views

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What is set theory?

asked Feb 2 in Mathematics by AstraNova Diamond (55.6k points) | 156 views

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How are equivalence relations used in mathematics?

asked Feb 2 in Mathematics by AstraNova Diamond (55.6k points) | 169 views

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What is the cardinality of the set of real numbers?

asked Feb 2 in Mathematics by AstraNova Diamond (55.6k points) | 156 views

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What is the cardinality of the set of natural numbers?

asked Feb 2 in Mathematics by AstraNova Diamond (55.6k points) | 172 views

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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 $F$.

asked Jan 30 in Mathematics by AstraNova Diamond (55.6k points) | 182 views

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Prove that the polynomial $x^5 - x^4 + x^3 - x^2 + x - 1$ is reducible over the integers.

asked Jan 27 in Mathematics by AstraNova Diamond (55.6k points) | 117 views

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Prove these trig expressions

asked Jan 24 in Mathematics by AstraNova Diamond (55.6k points) | 118 views

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Evaluate $\sum_{k=0}^8 2 k=$

asked Jan 21 in Mathematics by MathsGee Platinum (98.5k points) | 111 views

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Prove that the function $f(x) = \frac{1}{x}$ is uniformly continuous on the interval $(1,\infty)$.

asked Jan 10 in Mathematics by MathsGee Platinum (98.5k points) | 148 views

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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.

asked Jan 10 in Mathematics by MathsGee Platinum (98.5k points) | 122 views

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How important are aesthetics in mathematics?

asked Dec 29, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 202 views

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The model developed from sample data that has the form of $\hat{y}=b_0+b_1 x$ is known as

asked Dec 24, 2022 in Data Science & Statistics by MathsGee Platinum (98.5k points) | 144 views

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Define a function $f$ on the unit interval $0 \leq x \leq 1$ by the rule

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 194 views

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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?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 150 views

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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 $x$ ?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 172 views

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Let $T$ be the convex hull of the two current triangles. What is the volume of $T$ ?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 170 views

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How many quadratics are there with these properties?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 182 views

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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.)

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 150 views

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How many cool sequences are there?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 115 views

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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.

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 130 views

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Let $m$ and $n$ be positive integers such that $m^4-n^4=3439$. What is the value of $m n$ ?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 147 views

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Let $a_n=n(2 n+1)$. Evaluate \[ \left|\sum_{1 \leq j<k \leq 36} \sin \left(\frac{\pi}{6}\left(a_k-a_j\right)\right)\right| . \]

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 123 views

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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 $S$.

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 106 views

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Let $A B C D$ be the square face of a cube with edge length 2. A plane $P$ that contains $A$ and the midpoint of $\overline{B C}$ splits the cube into two pieces of the same volume.

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 97 views

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Let $\mathrm{X}=\{\mathrm{x} \in \mathrm{N}: 1 \leq \mathrm{x} \leq 17\}$ and $\mathrm{Y}=\{\mathrm{ax}+\mathrm{b}: \mathrm{x} \in \mathrm{X}$ and $\mathrm{a}, \mathrm{b} \in \mathrm{R}, \mathrm{a}>0\}$.

asked Nov 29, 2022 in Mathematics by Maths Genie Bronze Status (8.8k points) | 125 views

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If $R=\left\{(x, y): x, y \in Z, x^2+3 y^2 \leq 8\right\}$ is a relation on the set of integers $Z$, then the domain $R^{-1}$ is :

asked Nov 29, 2022 in Mathematics by Maths Genie Bronze Status (8.8k points) | 128 views

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Let $\mathrm{S}$ be the set of all $\lambda \in R$ for which the system of linear equations

asked Nov 29, 2022 in Mathematics by Maths Genie Bronze Status (8.8k points) | 178 views

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The integral $\int_0^2|| x-1|-x| d x$ is equal to :

asked Nov 29, 2022 in Mathematics by Maths Genie Bronze Status (8.8k points) | 156 views

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For a directed graph with a node $X$ : the parents of $X$ are a subset of the ancestors of $X$.

asked Nov 28, 2022 in Data Science & Statistics by MathsGee Platinum (98.5k points) | 156 views

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Complete: $2 x^2+3 x^2=\ldots$

asked Nov 27, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 128 views

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Complete: $\left(6^{2 / 3}\right)^3=\ldots$

asked Nov 27, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 100 views

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Complete: If $x=3$ the value of $y$ in the equation $y=4 x-3$ is $\ldots$

asked Nov 27, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 138 views

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Complete: $(a+b)^0=\ldots$

asked Nov 27, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 76 views

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Complete: In the expression $2 x-4$ the variable and constant are respectively: $\ldots$

asked Nov 27, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 91 views

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What are the requirements for a collection of items to be called a "set"?

asked Nov 27, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 160 views

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Why is it important to study set theory in mathematics?

asked Nov 27, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 262 views

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Let a set of 14 pairwise distinct positive integers be given. Prove that one can find two subsets $A=\left\{a_1, \ldots, a_k\right\}$ and $B=\left\{b_1, \ldots, b_k\right\}$ of this set with the same number ...

asked Nov 27, 2022 in Data Science & Statistics by MathsGee Platinum (98.5k points) | 168 views

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41 rooks are placed on a $10 \times 10$-chessboard. Prove that there are five rooks among these 41 that do not attack each other (i.e., no two of them are in the same horizontal or vertical line).

asked Nov 27, 2022 in Data Science & Statistics by MathsGee Platinum (98.5k points) | 161 views

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A set of $n$ disks $K_1, \ldots, K_n$ with radius $r$ is given in the plane. We know that no point of the plane is covered by more than 2003 of these disks.

asked Nov 27, 2022 in Data Science & Statistics by MathsGee Platinum (98.5k points) | 125 views

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Prove that there are 100000 South Africans that have the same birthday.

asked Nov 27, 2022 in Data Science & Statistics by MathsGee Platinum (98.5k points) | 224 views

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