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Questions tagged [proof-verification]

For questions concerning a specific proof or a specific solution, asking for verification, identifying errors, suggestions for improvement, etc. (You should not use this tag if the question does not contain a proposed proof/solution.)

For questions concerning a specific proof (or a proof sketch) or a solution to some problem; asking a question with this tag indicates one would like answers to respond broadly as to the following:

  • Verification of the proof/solution;
  • Identifying errors in the proof/solution;
  • Suggestions for improving the proof/solution;
  • Alternative approaches.

Also, consider the related tags and .

22798 questions
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Finding flaw in completed proof

I was given a complete proof and have to figure out the flaw that prevents the argument from being valid but I can't find it. I thought maybe it had something to do with replacing A and removing B but I am not sure. If anyone sees the error and can…
user503376
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Cardinality of a Function (Relation)

I need some assistance with the following problem: For $n \in \mathbb{N}$, let $A = \{a^1, a^2,a^3,...,a^n \}$ be a set and let $F$ be the set of all functions $f : A \rightarrow \{0,1 \}$ from $A$ to $\{0, 1\}$. What is the size of $F$? Now, for…
Sam Kay
  • 117
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Tricky, Interval Proof, is my Proof correct?

Prove that if x is in $[0,b]$, then $x=tb$ for some $t$ where $0 \le t \le 1$ My Attempt at a proof: Interval Midpoint: $ x = \frac{b}{2} $ $ \frac{b}{2} = tb $ $ \frac{1}{2} = t $ This is implies that value of $t$ is equal to $ \frac{1}{2} $ …
SFD
  • 145
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6 answers

Proof, Mathematical Induction concept

My prof. just taught us the method of mathematical induction today, and I'm still a little confused on the "Basis step" of the induction procedure. Why do we have to first prove that p(1) is true, if $p(n) = 3 \mid(n^4 - n^2)$, for all $n \in…
Sam Kay
  • 117
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2 answers

Prove that one element is bigger than or equal to the other.

I have the following two relations: 2^x =< (x+2)! and 2^(x+1) =< (x+3)! I assumed that the first statement is true and now, I'm trying to prove that the second statement is true too. I understand that I will have to substitute the first relation…
Jason Macville
  • 21
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Delta Epsilon Proof

I'm having a hard time solving this delta-epsilon proof. $$\lim_{x\to -2^+} x^4 = 16$$ Attached is my answer to the question, but apparently it is not correct and $\delta = {\epsilon \over 32}$ and not $\delta = {\epsilon\over 64}$. Can someone…
Hritik
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How do I solve for $x$ in the equation $x^3 - 8 = 0$ for which $x \neq 2?$

So my friend gives me a problem. Solve for $x$ in the following equation: $$x^3 - 8 = 0$$ So I did the following: $$\begin{align} x^3 \require{cancel}\cancel{- 8} \cancel{+ 8} &= 0 + 8 = 8 \\ x &= \sqrt [3] {8} = 2 \end{align}$$ Then my friend…
Mr Pie
  • 9,459
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2 answers

Let F be the following set F = ${(... \pm\frac{1}{2^3},\pm\frac{1}{2^2},\pm\frac{1}{2},0,1,\pm2,\pm2^2,\pm2^3....)}$

Not sure if I formatted it correctly, this is a screenshot of the question https://gyazo.com/75bb2ea6feb5babba9e60e081cdf8fb8 Let F be the following set $F = {{ (... \pm \frac{1}{2^3},\pm\frac{1}{2^2},\pm\frac{1}{2},0,1,\pm2,\pm2^2,\pm2^3...)}}$ Is…
user483618
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Is the following proof that $\sqrt2$ is irrational valid?

Given that all rational numbers have the following property: $\displaystyle\left\{ \frac{x}{y} \,\middle|\, x,y\in\mathbb Z\right\}$ it can be inferred therefore that $$\sqrt2=\frac{x}{y}$$ therefore $$2=\frac{x^2}{y^2}$$ and since $2=\frac{2}{1}$,…
joshuaheckroodt
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4 answers

How to prove $\sum _{i=1}^n\:\sum _{j=1}^n (i-j) = 0$

My professor didn't specify how we had to prove this but I'm assuming it should be done by induction. If not a point in the right direction would be much appreciated. Thank you.
Eddie White
  • 111
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Proof question involving primes and powers

I have a question about the following method... Q) Show that the number $2^{64} -1$ is not a prime. Working: If $2^{64} -1$ is a prime then it's only factors are 1 and itself $2^{64} -1 =(2^{32})^2 -1^2$ , using DOTS=$(2^{32}+1)(s^{32}-1)$ So…
Fred
  • 133
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Proof of $\sigma(-x) = 1 - \sigma(x)$. Is this correct?

In this video on Machine Learning, https://www.youtube.com/watch?v=ASn7ExxLZws , the lecturer suggests that it is good to try to prove this: $$\sigma(-x) = 1 - \sigma(x)$$ Where: $$\sigma(x) = \frac{1}{1 + e^{-x}}$$ I produced this proof. It is a…
TTransmit
  • 103
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proving the square of a number is the square of it's individual components

Given the number a: $\ a^2\ = H$, where H is a perfect square. Let : $\ a= c*d\ $, where c are it's prime factors. How do we prove that: $\ a^2\ $ = $\ (c * d)^2\ $ = $\ c^2 * d^2\ $
mathmaniage
  • 596
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4 answers

Proving $f(x)=x\cdot |x|$ is a bijection

Prove that the function $f: R\to R$ given $f(x)=x\cdot |x|$ is a bijection Proof 1: f is injective Suppose $$f(a) = f(b) \implies a\cdot |a| = b\cdot |b|$$ $$\implies (a\cdot |a|)^2 = (b\cdot |b|)^2$$ $$\implies a^4 =b^4$$ $$a=b$$ Thus, f is…
TheGamer
  • 393
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2 answers

$P \implies Q$ using proof by contrapositive

Let $x,y∈(0,1)$. Prove that if $x \ne y$, then $ \frac{x}{x^2+1} ≠ \frac{y}{y^2+1}$ Contrapositive: $\frac{x}{x^2+1} =\frac{y}{y^2+1} => x=y$ Suppose $¬Q$ happens $\frac{x}{x^2+1} =\frac{y}{y^2+1}$ $x(y^2+1) = y(x^2+1)$ $xy^2+x = yx^2+y$ $x=y$ How…
TheGamer
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