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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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Prove that if $A$ and $B$ are disjoint sets, then $P(A\cup B)\simeq P(A)\times P(B)$.

I feel that I didn't utilize the fact that A and B are disjoint in the proof below. Can anyone find the flaws in my proof? Suppose $A$ and $B$ are disjoint sets. Let $f : \mathcal P(A \cup B) \rightarrow \mathcal P(A) \times \mathcal P(B)$ be…
user231595
3
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3 answers

Prove if sup $S \in S \Rightarrow$ sup $S =$ max $S$

This is might be too easy, but just to make sure I am on the right track. Prove that if sup $S \in S \Rightarrow$ sup $S =$ max $S$ By definition, the maximum $max$ of a set $S$ is the number that is greater or equal to all the elements of $S$.…
user168764
3
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0 answers

Is my answer to this question wrong?

Let $k$ be a real number and let $f(x) := x^{2} + 2(k-2)x + k$. Find the range of $k$ if $\alpha > \beta$ are such that $f(x) = 0$ for $x = \alpha, \beta$ and if $\beta < -1 < \alpha.$ The given answer is $k < 1.$ However, I suspect it is wrong.…
Yes
  • 20,719
3
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3 answers

Is there a proof for the fact that, if you perform the same operation on both sides of an equality, then the equality holds?

Is there a proof for this, or is it just taken for granted? Does one need to prove it for every separate case (multiplication, addition, etc.), or only when you are operating with different elements (numbers, matrixes, etc.)?
Juanma Eloy
  • 1,407
2
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5 answers

Question about $i$

Was just fooling around with some identities and made this monster: Step (1) $i^{4} = 1$ Step (2) $ \sqrt[4]{i^{4}} = \sqrt[4]{1} $ Step (3) $i = 1$ Step (4) $\sqrt{-1} = 1$ What did I do wrong here? Update: Thank you! All of you. For your time and…
Joe
  • 31
2
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1 answer

Short clarification on induction prove with Gamma defnition

Suppose we are asked to prove this one using induction: $$k! = \int_0^\infty e^{-x}x^{k} dx \,\,\, (*)$$ For $k=0$, it is clear after evaluating the appropriate improper integral that, $$0! = \int_0^{\infty} e^{-x} dx = 1$$ For the induction case,…
vTx
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2 answers

Proving disconnected sets.

I came up with two weak incomplete solutions to the problem. If $E$ and $F$ are connected subsets of a metric space $M$ with $E \cap F \neq \emptyset$. Show $E \cup F$ is connected. failed proof1: If $E \cup F$ is not connected, let $W$ and $V$ be…
Lemon
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2 answers

Is it true that $3$ is the only prime of the form $n^2-1$?

One less than a perfect square is prime if and only if the prime is 3. Is this really, really true and do we have proof?
Jeffrey Young
  • 841
2
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2 answers

Proof that odd + odd = even

In math class today we started talking about proofs that odd + odd is even. We went over the basic proof (using 2k+1 and equations etc) and I realized that the only reason that this property exists is because the distance between two consecutive…
thequantumguy01
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2 answers

Proof About Division of Integers

Here is a problem I just finished working on: Prove that if $n$ is composite then there are integers $a$ and $b$ such that $n$ divides $ab$ but not $n$ does not divide either $a$ or $b$. One thing I noticed while proving this is, that we are…
Mack
  • 4,639
2
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3 answers

If 1 $\leq x$, then $\sqrt{x} \leq x $

This is a really simple problem but I am unsure if I have proved it properly. By contradiction: Suppose that $x \geq 1$ and $x< \sqrt{x}$. Then $x\cdot x \geq x \cdot 1$ and $x^2 < x$ (squaring both sides), which is a contradiction.
grayQuant
  • 2,619
2
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3 answers

Need opinion on proof (if $ax=a$, then $x=1$)

I haven't written a lot of proofs so I need the opinion of the experts on my proof of a simple proposition. Here's the various properties I used: (P10) (Trichotomy law) For every number $a$, one and only one of the following holds: (i) $a = 0$, (ii)…
user108343
2
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0 answers

Kelly Criterion with known expected gain of a winning bet.

lately I am busy with working through the Paper of Kelly concerning "A New Interpretation of Information Rate" for the purpose of moneymanagement in Trading. http://pnaelvlinux.net/brokerage/kelly.pdf In his Paper he introduces the following formula…
CCommander
  • 21
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1 answer

Proving is $x+1$ is even, then $x$ is odd

Suppose that $x+1$ is even, such that there exists and integer $k$ such that $x+1=2k$. $$x+1 = 2k\implies x=2k-1$$ since $k$ is an integer and $L+1$ is also an integer $k := L+1$ $$x=2(L+1)-1 \implies x=2L+2-1 \implies x=2L+1$$ Since $x$ follows…
Thomas
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