Recent questions tagged proof

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How does the forever affiliate option in Acalytica work?

asked Aug 27 in Link-in-Bio by MathsGee Platinum (98.5k points) | 13 views

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How do I add social proof or badges to my Acalytica page?

asked Aug 22 in Link-in-Bio by MathsGee Platinum (98.5k points) | 16 views

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Is there a referral program for Acalytica?

asked Aug 22 in Link-in-Bio by MathsGee Platinum (98.5k points) | 6 views

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What is the point of adding social proof widgets on my website?

asked Aug 9 in Advertising & Marketing by MathsGee Platinum (98.5k points) | 22 views

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What is an algebraic proof?

asked May 23 in Mathematics by MathsGee Platinum (98.5k points) | 118 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 social proof marketing?

asked May 1 in Advertising & Marketing by MathsGee Platinum (98.5k points) | 158 views

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How can platforms create mechanisms for "proof of personhood" to post?

asked Mar 13 in Artificial Intelligence by MathsGee Platinum (98.5k points) | 234 views

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How does an argument differ from a proof in mathematical logic?

asked Feb 2 in Mathematics by AstraNova Diamond (55.6k points) | 186 views

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What is the rank of a matrix?

asked Jan 27 in Mathematics by AstraNova Diamond (55.6k points) | 183 views

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Calculate, by using an appropriate formula: $3-1+\frac{1}{3}-\ldots \ldots \ldots \ldots \ldots+\frac{1}{243}$

asked Jan 21 in Mathematics by MathsGee Platinum (98.5k points) | 133 views

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Does Acalytica Social Proof have an affiliate/referral program?

asked Oct 23, 2022 in General Knowledge by MathsGee Platinum (98.5k points) | 154 views

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What are the different types of social proof?

asked Oct 12, 2022 in General Knowledge by MathsGee Platinum (98.5k points) | 278 views

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What is social proof?

asked Oct 12, 2022 in General Knowledge by MathsGee Platinum (98.5k points) | 280 views

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Let $0 \leq x_{i, j} \leq 1$, where $i=1, \ldots, m, j=1, \ldots, n$. Prove the inequality

asked Sep 23, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 118 views

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The number $10^{2007}$ is written on the blackboard. Anne and Berit play a two-player game in which the player in turn performs one of the following two operations:

asked Sep 23, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 104 views

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Given a finite sequence $x_{1,1}, x_{2,1}, \ldots, x_{n, 1}$ of integers ( $n \geq 2$ ), not all equal, define the sequences $x_{1, k}, \ldots, x_{n, k}$ by

asked Sep 23, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 126 views

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Prove that \[ \frac{1}{2^2}+\frac{1}{3^2}+\cdots+\frac{1}{n^2}<\frac{2}{3} \] for all $n \geq 2$

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 71 views

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Prove that \[ \frac{1}{2^2}+\frac{1}{3^2}+\cdots+\frac{1}{n^2}<\frac{2}{3} \] for all $n \geq 2$

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 61 views

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One writes 268 numbers around a circle such that the sum of 20 consecutive numbers is always equal to 75 . The numbers 3,4 and 9 are written in positions 17,83 and 144 respectively. Find the number in position 210.

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 167 views

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Prove the inequality $a^2+b^2+c^2 \geq a b+b c+c a$, if $a, b, c$ are real numbers.

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 126 views

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Find the mistake in this proof

asked Sep 15, 2022 in General Knowledge by AstraNova Diamond (55.6k points) | 159 views

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Are all numbers real?

asked Sep 7, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 128 views

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What are real numbers?

asked Sep 7, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 129 views

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Suppose that $x_{1}, x_{2}, \ldots, x_{n}, y_{1}, y_{2}, \ldots, y_{n}$ are real numbers such that $x_{1} \leq x_{2} \leq \cdots \leq x_{n}$ and $y_{1} \leq y_{2} \leq \cdots \leq y_{n}$.

asked Jul 29, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 200 views

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Suppose that $x_{1}, x_{2}, \ldots, x_{n}$ are positive real numbers. Prove that \[ \frac{x_{1}}{x_{2}}+\frac{x_{2}}{x_{3}}+\cdots+\frac{x_{n-1}}{x_{n}}+\frac{x_{n}}{x_{1}} \geq n . \]

asked Jul 29, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 253 views

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Suppose that $a_{1}, a_{2}, \ldots, a_{n}$ are real numbers such that $a_{i} \geq 1$ for all $i$. Prove the inequality

asked Jul 29, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 212 views

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Suppose that $x_{1}, x_{2}, \ldots, x_{n}$ are real numbers such that $0 \leq x_{i} \leq 1$ for all $i$. Prove that

asked Jul 29, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 202 views

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Suppose that $x_{1}, x_{2}, \ldots, x_{n}$ are real numbers such that $0 \leq x_{i} \leq 1$ for all $i$. What is the maximum possible value of \[ \sum_{i=1}^{n} \sum_{j=1}^{n}\left(x_{i}-x_{j}\right)^{2} \]

asked Jul 29, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 240 views

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Define a sequence $a_{1}, a_{2}, \ldots$ by $a_{1}=\frac{5}{2}$ and $a_{n+1}=a_{n}^{2}-2$ for $n \geq 1$. Give an explicit formula for $a_{n}$ and prove it.

asked Jul 29, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 197 views

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30 numbers $a_{1}, \ldots, a_{30}$ are written along the circle in such a way that each of them is equal to the absolute value of the difference between the next two in the clockwise direction

asked Jul 28, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 126 views

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What is an absolute value in mathematics?

asked Jul 19, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 205 views

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Let $a_{0}=6$ and \[ a_{n}=\frac{a_{n-1}}{1+a_{n-1}} \] for all $n \geq 1$. Find $a_{100}$.

asked Jul 7, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 145 views

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Assume $A \in L(X, Y)$ and $A \mathbf{x}=0$ only when $\mathbf{x}=0$. Prove that $A$ is then 1-1.

asked Jul 5, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 194 views

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If $k$ sets of data consist, respectively, of $n_{1}, n_{2}, \ldots, n_{k}$ observations and have the means $\bar{x}_{1}, \bar{x}_{2}, \ldots, \bar{x}_{k}$, then the overall mean of all the data is given by the formula

asked Jun 17, 2022 in Data Science & Statistics by AstraNova Diamond (55.6k points) | 200 views

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If data are coded so that $x_{i}=c \cdot u_{i}+a$, show that $\bar{x}=c \cdot \bar{u}+a$ and $s_{x}=|c| \cdot s_{u}$.

asked Jun 17, 2022 in Data Science & Statistics by AstraNova Diamond (55.6k points) | 74 views

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Show that \[ \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)=0 \] for any set of observations $x_{1}, x_{2}, \ldots, x_{n}$.

asked Jun 17, 2022 in Data Science & Statistics by AstraNova Diamond (55.6k points) | 149 views

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Prove that a prime number cannot be a perfect number.

asked Jun 4, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 426 views

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Prove the theorem of Pythagoras $T P^{2}=P R^{2}+T R^{2}$

asked Apr 17, 2022 in Mathematics by AstraNova Diamond (55.6k points) | 206 views

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What is a mathematical statement?

asked Feb 3, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 286 views

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If $\mathbf{v}$ is a vector in $R^{n}$, and if $k$ is any scalar, then prove that $\|\mathbf{v}\|=0$ if and only if $\mathbf{v}=\mathbf{0}$

asked Jan 26, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 541 views

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If $\mathbf{v}$ is a vector in $R^{n}$, and if $k$ is any scalar, then prove that $\|\mathbf{v}\| \geq 0$

asked Jan 26, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 451 views

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Prove that if $\mathbf{u}, \mathbf{v}$, and $\mathbf{w}$ are vectors in $R^{n}$, and if $k$ is a scalar, then $(\mathbf{u}+\mathbf{v}) \cdot \mathbf{w}=\mathbf{u} \cdot \mathbf{w}+\mathbf{v} \cdot \mathbf{w}$

asked Jan 26, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 501 views

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Prove that if $\mathbf{u}, \mathbf{v}$, and $\mathbf{w}$ are vectors in $R^{n}$, then:

asked Jan 26, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 537 views

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Say you have $k$ linear algebraic equations in $n$ variables; in matrix form we write $A X=Y$. Give a proof or counterexample for each of the following.

asked Jan 21, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 365 views

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Let $A=\left(a_{i j}\right)$ be an $n \times n$ matrix with the property that its absolute row sums are at most 1 , that is, $\left|a_{i 1}\right|+\cdots+\left|a_{\text {in }}\right| \leq 1$ for all $i=1, \ldots, n$.

asked Jan 21, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 300 views

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Let $A$ be a square matrix and let $\|B\|$ be any norm on matrices [one example is $\left.\|B\|=\max _{i, j}\left|b_{i j}\right|\right]$.

asked Jan 21, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 363 views

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Let $A$ be a square matrix. In the following, a sequence of matrices $C_{j}$ converges if all of its elements converge.

asked Jan 21, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 289 views

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Let $\alpha_{1}, \ldots, \alpha_{n}$ be positive real numbers and let $A=\left(a_{i j}\right)$ where $a_{i j}=\alpha_{i} / \alpha_{j} .$ Say as much as you can about the eigenvalues and eigenvectors of $A$.

asked Jan 21, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 377 views

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Show that $p(\lambda)=\lambda^{n}+a_{n-1} \lambda^{n-1}+\cdots+a_{0}$ is the characteristic polynomial of the matrix

asked Jan 21, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 343 views

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