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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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A metric $X$ is compact iff every continuous function on $\mathbb{R}$ attains maximum and minimum values

Let $(X,d)$ be compact and $f:X \rightarrow \mathbb{R}$ be continuous. Then if $X$ is compact, $f(X)$ is also compact. Compact subsets of $\mathbb{R}$ are closed and bounded. By the completeness axiom $f(X)$ must have a lowest upper bound and…
Cococabana
  • 173
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1 answer

Proof that countable infinite set is equitotient to $\mathbb{N}$

So I wanna show that if $Y$ is an infinite countable set (i.e. there exists a surjection $\phi: \mathbb{N} \to A$), then there exists a bijection $\psi: \mathbb{N} \to A$. Here's what I came up with. Define a sequence of maps $f_{i} : \mathbb{N} \to…
AJY
  • 8,729
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0 answers

Let $p$ be a prime. Let $f(x) = 3x+1$ and $g(x) = 6x+1$. Show that if $f(x) = p$, then $g(y) = p$.

The full question states: Let $p$ be a prime. Let $f(x) = 3x+1$ and $g(x) = 6x+1$. Show that: if there exists $x\in \Bbb N$ such that $f(x) = p$, then there exists $y\in \Bbb N$ $g(y) = p$. My attempt at this was quite simple. I said that as $p$…
L. Murphy
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Given (A => B) => C , B, prove C with resolution method

So with the premises $(A \Rightarrow B) \Rightarrow C$ $B$ It is easy to prove $C$ in the Fitch method, as in the proof below proof Therefore I should be able to prove it using a resolution proof $(A \Rightarrow B) \Rightarrow C$ $\neg (A…
jimboweb
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1 answer

Is my proof for $\sqrt{2}$ Irrationality correct?

I use strong induction on $p$. Proof: We want to show that $\forall q\in \mathbb{N} \big[q>0 \rightarrow \neg\exists p\in\mathbb{N}\big(p/q=\sqrt{2}\big)\big]$. Let $q$ be arbitrary natural number and $q>0$. Inductive Hypothesis : Let…
KeyC0de
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3 answers

Is a fraction number may be negative or not?

We know that A fraction represents a part of a whole or, more generally, any number of equal parts. So fraction can not be negative.$\frac12$ and $\frac{-1}{2}$ both are fraction number or not?
user293607
  • 101
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1 answer

How to prove equality with exponential function

How to prove this equality: $$\frac{1-e^{-\frac{1}{t}}}{1-e^{-\frac{1}{2t}}}=1+e^{-\frac{1}{2t}}$$ I've no idea how to start so everything is welcome! Thanks a lot!
user294478
2
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5 answers

Is my proof of $-(-a)=a$ correct?

I'm trying to prove theorem $1.4$ with the following: $$a=a$$ $$a-a=\stackrel{0}{\overline{a-a}}\tag{Ax.5}$$ $$a-a=0\tag{Inverse def.}$$ $$a+(-a)=0\tag{Thm 1.3}$$ Here I thought about packing the $a$ with a minus sign and then it would yield a…
Red Banana
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Ignoring convergence issues to obtain an integral

This is related to this question. Let $$f(t) = \int_0^1 \frac{x \ln(x)}{(x^2+t)^2} dx$$ so that we want $f(1)$. (The answer turns out to be $-\frac{1}{4} \log(2)$.) Then $$f'(t) = -2 \int_0^1 \frac{x \ln(x)}{(x^2+t)^3} dx$$ and in general we get…
Patrick Stevens
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2 answers

proof about integer being written as two integer squares

Problem: If $q$ is an integer that can be expressed as the sum of integer squares,show that both $2q$ and $5q$ can also be espressed as the sum of two integer squares.
Nameless
  • 1,480
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4 answers

Prove that if $A$, $B$ are countable, then $A \times B$ is countable?

Is $A\times B$ referring to the axis here? So an $X$ and $Y$ coordinate plane? $A$ is countable, therefore a bijection occurs from $A \rightarrow \mathbb{N}$. $B$ is countable, therefore a bijection occurs from $B \rightarrow \mathbb{N}$. If these…
Eddard
  • 65
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3 answers

Let $A = \mathbb{Z}$, $B = [−1, \pi]$, $C = (2, 7)$. List all elements of $A \cap (B^c \cap C)$.

After working it out on a number line, I got: $\{4, 5, 6\}$. As it stands, the expression contains the integers that do not belong to the set $B$ that cross into $C$. This would result in $4, 5, 6$. Number $7$ would not be included because of the…
Eddard
  • 65
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1 answer

Proof-verification: Bolzano Weierstrass theorem (modified)

I want to show that every bounded sequence has a subsequence that converge. Do you agree with my proof and if not, what's wrong ? Proof Let $(x_n)_{n\in\mathbb N^*}$ a bounded sequence. Since $(x_n)_{n\in\mathbb N^*}$ is bounded,…
idm
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2 answers

If both $f$ and $g$ are not integrable, then $f+g$ and $fg$ are not integrable

If both $f$ and $g$ are not integrable, then $f+g$ is not integrable I think this is false. Take $f(x) = \begin{cases} 1 & \text{ if } x \in \mathbb{Q} \\ 0 & \text{ if } x \in \mathbb{Q}^c \end{cases}$ and $g(x) = \begin{cases} 1 & \text{ if } x…
Adrian
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0 answers

Verification of a trivial proof

Sorry for this dumb question, I know it's a very simple statement but my proof was different from the one given in the notes, and 9 out of 10 times when I try to write proofs myself they turn out to be incorrect, so I would just like to know if my…
Vizuna
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