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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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Even and Odd proof: Direct proof conflict with Counter example

Question: If $n \in \mathbb{Z}$ and $n^5 − n$ is even, then $n$ is even. My solution: By counter example, let $n = 3$, then $3^5 - 3 = 240 =$ even, but $3 =$ odd. However, if I use direct proof on this, it will be: Suppose $n \in \mathbb{Z}$ and…
Sam Kay
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Show that for every $n$, there exists a number with $0$'s and $7$'s such that $n$ divides it

Show that for every $n$, there exists a number with $0$'s and $7$'s such that $n$ divides it. My proof goes as follows: Consider the set of integers $\{10^0, 10^1, 10^2, \cdots, 10^n\}$. It's fairly obvious by $\textbf{PHP}$ that $\exists \text {…
Mathejunior
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Prove that $x^2 + 3 > 2x + 1$ for all values of $x$

how would I go about proving this: $x^2 + 3 > 2x + 1$ I know that I have to complete the square but do I bring everything to one side and convert it to an equation or do I simply complete the first side? Sorry if this seems nooby
Praveen K
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Prove that if $x^3 - x > 0$, then $x > -1$

I know this probably seems like an easy problem, but I generally struggle with inequalities, so I was looking to see if someone could verify that the following proof of mine is correct. This was an even problem in my book, so no answers are…
Aleksandr Hovhannisyan
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Prove that if $a$ and $b$ are integers with $a\not= 0$ and $x$ is a positive integer such that $ax^2 + bx + b − a = 0$, then $a|b$.

Prove that if $a$ and $b$ are integers with $a\not= 0$ and $x$ is a positive integer such that $ax^2 + bx + b − a = 0$, then $a|b$. I will use the backwards and forwards method to prove the proposition. A represents the hypothesis, and B represents…
The Pointer
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Is this valid way to prove $(-1)(-1) = 1$?

$(1-2)(1-2) =1-2-2+4=1$, using the distributive property. If it's not valid, why?
user3000482
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Show that $(n!+1,(n+1)!+1)=1$.

Problem: Show that $(n!+1,(n+1)!+1)=1$. My Attempt: Let $(n!+1,(n+1)!+1)=e$. Then: $$(n!+1,(n+1)!+1)=(n!+1,(n+1)!+1-((n+1)!+n+1)=(n!+1,-n)$$ $=(n!+1,n)\Rightarrow n=ek_1$ and $n!+1=ek_2$ for some $k_1$ and $k_2$ in $\mathbb{Z}$. Observe that…
Student
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Is my proof that $x^2+y^2+z^2 ≥ xy+yz+xz$ correct?

The question: Prove that $x^2+y^2+z^2 ≥ xy+yz+xz$ for all real numbers $x$, $y$ and $z$. This problem has been posed before, but my question is whether my proof below is correct, since it seems the other answers to this problem are different. If…
wrb98
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Show that certain relation is or is not a total order

Suppose $R$ is a total order on $A$ and $S$ is a total order on $B$. Define a relation $L$ on $A \times B$ as follows: $L = \{((a, b), (a', b')) \in (A \times B) \times (A \times B) | aRa' \land (a = a' \implies bSb') \}$. Is $L$ a total order?…
pseudomarvin
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Prove that if $A$ has the same cardinality as $\emptyset $, then $A= \emptyset$

Let Equivalence($\equiv$) be defined as having the same cardinality. Assume, $A \equiv \emptyset $. Then, there exists a function $f: A \to \emptyset $ such that f is a bijection. This proof will now proceed by contradiction. Suppose, $ A \ne…
user223868
3
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2 answers

Show that the fourth power of every odd integer is of the form $16k+1$.

This is what I have so far, I'm not sure my reasoning is correct as I am trying to learn how to construct proofs. I would appreciate any feedback on if I took the right steps. If there is an alternative way of going about this problem, what would it…
Curious Math Student
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Where is the fault in my proof?

I had some spare time, so I was just doing random equations, then accidentally came up with a proof that showed that i was -1. I know this is wrong, but I can't find where I went wrong. Could someone point out where a mathematical error was…
RK01
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Solving an equation, need help with explaining why one solution cant be true

I have solved the equation $$\sqrt{\frac{2}{x}}-\sqrt{\frac{x}{2}}=\frac{1}{\sqrt{2}}$$ where $x$ is $x=1$ and $x=4$. My question is why can't $x=4$? I understand that the equation does not hold if I put $4$ in the equation instead of $x$. Is there…
Ophelia Lindberg
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2 answers

Help with an inductive proof of $(1+a)^n\ge 1+na$

Let $a$ be a fixed real number such that $a > -1$. Prove $(1+a)^n \geq 1+an$ for any $n\in\mathbb{N}$. Base case. $n = 1$. $(1+a)^1 = 1+a(1)$ $\implies 1+a = 1+a$. $1+a = 1+a(1)$. so we can assume $P(n)$ is true when $n = 1$. Want to show $P(n+1)$…
J00S
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Does the proportion pass through 1/2?

Michael Jordan is shooting free throws. He misses his first one. At the end of the day, he has made $99$% of his free throws. At some point during the day, did he necessarily have a $50$% success rate? My Attempt Since he started at $0$% and made…
user01101001
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