Questions tagged [solution-verification]

For posts looking for feedback or verification of a proposed solution. "Is my proof correct?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.

This tag should be used when you have a proposed solution to a problem and have specific concerns or doubts about the validity of that solution. A question with this tag should include an explanation for why the argument presented is not convincing enough. Further discussion on using this tag can be found in the Mathematics Meta questions (1) and (2).

Answers to questions tagged look first and foremost to check that the solution is right, and to comment upon the approach taken by the author of the question. If the proposed solution is wrong, a good answer would explain where or how mistakes were made, and possibly give or sketch a correct solution instead.

If the proposed solution is correct, an answer would ideally provide further evidence to back the answerer's opinion. These could include a clearer rewriting of the given argument, alternative arguments, generalizations of the proven result, or careful consideration of unexpected subtle points. Users looking to write answers can find further discussion in this Mathematics Meta post.

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Why is $n = k+1$ in $\frac{d^ny}{dx^n} = (\frac{d}{dx})(\frac{d^{k-1}y}{dx^{k-1}})$ and not $\frac{d^{k+1}y}{dx^{k+1}}$?

The question stems from the following mathematical induction: However, the solution I found here…
user71207
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How do prove $12^n - 4^n - 3^n +1$ is divisible by 6 using mathematical induction, where n is integral?

So this question is very challenging because normally the bases of the exponents are the same. There are too many different bases for me to successfully subtitue in the assumption (when $n=k$) I was hoping someone out there will have a super smart…
user71207
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Cosine rule formula proof problem with do product, where does positive sign come from?

I if want to prove the cosine rule with the vector summation (such as I have mentioned in the picture) I start with the…
John Jin
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Identity Element of Subtraction (Solution Verification)

This is about an exercise from Norman L. Biggs Discrete Mathematics. One is asked to check which binary operations are valid when $*$ represents the usual $-$ of arithmetic. Now, Biggs says that $-$ has an identity value. But, using the…
user0233
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Please help me with this: card([m])=card([n]) implies m = n

Can someone read my parts (a) to (d)? I think they're good - however, I'm really stuck on part (e) and would love some help. Definition: 2 sets X and Y have the same cardinality (card(X)=card(Y)) if there exists a bijection f: X --> Y. Let $m,n\ge1$…
beginner
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Let $x,y \in \mathbb{R}^+$, prove that if $x \leq y$ then $x^2 \leq y^2$

I just started to learn how to do proofs, and I'm trying to solve this exercise, I have to do it by direct proof and by contradiction. The proof of my book is: Direct proof: Let $x,y \in \mathbb{R}^+$ such that $x \leq y$. Multiplying both sides by…
pipey
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Prove if xy < 140 then x < 10 or y< 14 by Contraposition

I have the following proof for this statement - Assume $x$ and $y$ are both integers. Prove by contraposition, if $xy < 140$ then $x < 10$ or $y< 14$. Assume that $x ⩾ 10$ and $y ⩾ 14$, then $xy ⩾ 10\cdot14 = 140$ My attempt at a proof is as…
Scott Adamson
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Why $\frac{|Ap+Bq+C|}{\sqrt{A^2+B^2}}$ is the shortest distance from a point$(p,q)$ to a line equation $Ax+By+C=0$?

I want to show the statement "Let $(h,k)$ be a point on a line $Ax+By+C=0$ prove that $\sqrt{(h-p)^2+(k-q)^2}$ $\geq$ $\frac{|Ap+Bq+C|}{\sqrt{A^2+B^2}}$" is true. I do try to prove it with contradiction. Proof Suppose $(h,k)$ is a point on the…
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Spivak Calculus Chapter 1 Question 18 b

I have recently started to self-study Spivak's Calculus book, and to be honest, my math is kind of rusty so I was just wanting to confirm that I have done this question correctly. The question: Suppose that $b^2 -4c < 0$. Show that there are no…
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Prove that $\lim_{n \to \infty} \sqrt{a_n} = \sqrt{L}$

$1.$ Let $\{a_n\}$ be a sequence of positive terms such that $\lim_{n \to \infty} a_n = L$ where $L > 0$. Prove that $\lim_{n \to \infty} \sqrt{a_n} = \sqrt{L}$. Proof of $1:$ \begin{align*} \forall \epsilon > 0\: \exists N >0\:\: s.t\:\:n>N …
Nimantha
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Substitution for equation in two variables

Lets say I start with an equation $$3(1+x+x^2)(1+y+y^2)(1+z+z^2)=4x^2y^2z^2-1$$ and I get a solution in positive integers $(4,4^3,4^6)$. To go about showing that there are no solutions possible in odd positive integers $x_0,y_0,z_0$ I perform a…
thestar
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Show that the sequence $\{a_n\}$ converges where $a_1 = 1$ and $a_n = \sqrt{1+ a_{n-1}}$ for all $n \geq 2$. With MCT and induction.

Not only will I prove this, but I will further use the property of subsequences to find the limit of the sequence. 1. We must show that $a_n$ is monotone increasing or decreasing, and 2. that $a_n$ is bounded (above or below). By inspection, $a_1…
thomasbdc
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The Connectedness of Interiors and Closures (Proof Verification)

I'm practicing my proof-writing and was hoping you could let me know if this proof looks good. I would like to know if the proof is incorrect, if there are parts that are overly wordy/complicated, or if I'm missing some element of a proof that is…
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Prove that a set of sequences is countable (Proof Verification)

I'm practicing my proof-writing and was hoping you could let me know if this proof looks good. I would like to know if the proof is incorrect, if there are parts that are overly wordy/complicated, or if I'm missing some element of a proof that is…
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$e^{-xy} + e^{xy} = 2e^{-y}$ - where am I going wrong?

I am trying to see if there is any $x$ (real or complex) for which this equation can be solved. $$e^{-xy} + e^{xy} = 2e^{-y}$$ Step 1. Multiplying both sides by y, $$ye^{-xy} + ye^{xy} = 2ye^{-y}$$ Step2. Partially differentiating the original…
Srini
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