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Mathematics Stack Exchange

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 .

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Prove that between two unequal rational numbers there is another rational

I understand that I probably asked a question that the users of this site would view as elementary, but I have only just dipped my feet into the waters of proof solving. Can somebody please tell me if my proof is valid? Let there be two rational…
Murph Jones
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Proving/disproving that √7 - √2 is irrational

It's been proven that √7 and √2 are irrational. However, I am not sure how to go about proving that √7 - √2. Is it an acceptable proof to just solve the equation which would prove/disprove the equation or as should the proof be done as a…
Jessica Tiberio
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Maximum number of real roots of this equation

Question: What is the maximum number of real roots for this equation? Assume $a,b,c$ are positive real numbers. $$(ax^2+bx+c)(bx^2+cx+a)(cx^2+ax+b)=0$$ My attempt: Let us assume the equation has 6 real roots. So, the discriminants are…
Gaurang Tandon
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Prove the following $x^2−y^2=(x−y)(x+y)$

I'm going through the book Calculus by Michael Spivak, not sure on how to go about the first problem. If anyone can just go through it with a solution I think I can handle myself from there. Thanks. Prove the following: $x^2−y^2=(x−y)(x+y)$
Alexander John
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Prove that there exists rational numbers $x$ such that $\sqrt{x + 2016}$ and $\sqrt{x + 2017}$ are also rational

I need to know if my solution is correct. Here is how I did it: By substituting $x + 2016$ with $t$, our problem reduces to proving that there exists $t \in \mathbb{Q}$ such that $\sqrt t$ and $\sqrt {t + 1}$ are rational numbers. Let $t =…
George R.
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Can someone explain this proof of the product property of square roots?

I'm studying a proof of the product property of square roots. I can follow it up to statement 8, but I can't make sense of how the last statement, 9, follows from the previous ones. I have transcribed the proof below. Product property of square…
Chrisuu
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Proof that an infinite subset of $\mathbb{N}$ is countable

I want to prove that if $A$ is an infinite subset of the natural numbers, then it is countable. I thought of an informal proof: put the elements of $A$ in increasing order. Then associate the smallest to $1$, the second smallest to $2$, the third…
Adrian
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$\sqrt{ab} = \sqrt{a} \sqrt{b}$

I'm trying to show that $\sqrt{ab} = \sqrt{a} \sqrt{b}$ where $a, b > 0$ For contradiction assume $$\sqrt{ab} \not= \sqrt{a} \sqrt{b}$$ $$ \sqrt{ab} - \sqrt{a} \sqrt{b} \not=0 $$ $$ \left(\sqrt{ab} + \sqrt{a} \sqrt{b}\right) \left(\sqrt{ab} -…
Jack
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How to prove the following bounds expression

Let n be a positive integer. Prove that there are 2^(n−1) ways to write n as a sum of positive integers, where the order of the sum matters. For example, there are 8 ways to write 4 as the sum of positive integers: 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 2 +…
MichaelGofron
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A simple proof varification

A certain pipe can fill a swimming pool in $2$ hours; another pipe can fill it in $5$ hours; a third pipe can empty the pool in $6$ hours. With all three pipes turned on exactly at the same time, and starting with an empty pool, how long will it…
Mathslover
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Prove that a horizontal asymptote can never be crossed

This is a lot simpler of a problem than others posted here, but I was bored in class and decided to work out why a horizontal asymptote exists. Bear in mind that I am still fairly low on the “math ladder.” So to accomplish this I worked off of one…
Jake R
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Find a formula for the number of solutions to...

Find a formula for the number of solutions to $$ x_1 + x_2 + x_3 + \ldots + x_k = n $$ where $n \ge 0$ and the the $x_i$ are non-negative integers. For instance, if $n > 0$ then there is exactly one solution to $x_1 = n$. There are $n + 1$ solutions…
anonymous9254
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If $2^X = 2^Y$ then, $X=Y$?

I'm blocked on a question about sets: if $2^X= 2^Y$ holds for two sets $X$ and $Y$, then can we say that $X=Y$ ? I know how to prove it with two integers a and b but how can i show it with two sets? Thanks
Tom92
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$\pi = 0$! It can't be!

Keep in mind: I'm still in high-school so forgive my poor maths. Also remember that I'm in HIGH-SCHOOL so nothing to complex I like to mess around with equations and I find it quite fascinating the results I can somehow come up with. Recently, I…
caird coinheringaahing
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Proving there is no rational number such that square of it is equal to 2.

I start the proof by assuming there is $m/n \in Q$, expressed in lowest terms, such that $$(m/n)^2=2$$ My textbook tells me to derive a contradiction by showing $m,n$ are both even. Here's how I did it. $(m/n)^2=2$ $m^2/n^2=2$ $m^2=2n^2$ Hence,…
user3000482
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