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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.

21426 questions
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Proof on inequality $|x-1|$

I had an inequality problem when dealing with proof $0\lt|x-1|\lt a$, then $|x-1||x-1|\lt a^{2}$ ? does this sound right?
JungleKing
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Solution Verification - Area between a Curve

Conflicted on whether I did this correctly. Any suggestions are appreciated!
Eight 8
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Could you suggest me that can I prove " For every $x$ $\in$ $[\frac{\pi}{2},\pi]$, $\sin(x)-\cos(x) $ $\geq$ $1$ " like this?

Can I prove " For every $x$ $\in$ $[\frac{\pi}{2},\pi]$, $\sin(x)-\cos(x) $ $\geq$ $1$ " like this? Proof For the sake of contradiction suppose $x$ $\in$ $[\frac{\pi}{2},\pi]$ for which $\sin(x)-\cos(x) $ $<$ $1$ When $x$ $\in$…
Mathskid
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Is this proof of Bernoulli’s inequality correct?

I have to prove $(1+x)^{n} >1+nx$ for $n=2,3,4.... $and $x>-1$ and $x$ isnt 0. There are a lot of proofs of this but l want to know if this one works. If not, can u show where my reasoning is weak. If $x>-1$ then $1+x>0$ Hence $ (1+x)^{n}>0$ for…
Aristotle Stagiritis
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Simple algebraic proof for Mohr circle

In attempting to derive the Mohr circle equations and given $$ \sigma_N=\sigma_1n_1^2+\sigma_2n_2^2+\sigma_3n_3^2\tag{1}$$ $$\sigma_n^2+\sigma_S^2=\sigma_1^2n_1^2+\sigma_2^2n_2^2+\sigma_3^2n_3^2\tag{2} $$ $$n_1^2+n_2^2+n_3^2=1\tag{3},$$ how does one…
Rodrigues
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Prove that n^3 - n is a multiple of 6 for all positive integral values of n

Prove that $$n^3 - n$$ is a multiple of 6 for all positive integral values of n Does positive integral values of n refer to values of n once the expression is integrated to $$1/4n^4 - 1/2n + c$$ How do you deal with the constant of integration in…
FelixM
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Find all integers such that $\sqrt{(n-4)\sqrt{n-19}}$ is also an integer.

This is my solution not sure if it is correct though. Solution: For the expression to be an integer, $(n-4)\sqrt{n-19}$ should be a perfect square. For $(n-4)\sqrt{n-19}$ to be a perfect square, $(n-4)^2(n-19)$ should be a perfect square. Now…
Khant Rain
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Proving that $\sum_{j=0}^n {n \choose j} = {n \choose 0} + ... + {n \choose n} = 2^n$

I'm looking for a proof verification, precisely at the end of the proof. We proceed by induction on $n$. Pf. Base case $n = 1$,$$\sum_{j=0}^1 {1 \choose j} = {1 \choose 0} + {1 \choose 1} = 1 + 1 = 2^1$$ Notice also for $n=2$, $$\sum_{j=0}^2 {2…
dan
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Proof of ∀(x,y)∈R[|x-y| ≥ |x| - |y|]

Is the following proof correct? To prove: ∀(x,y)∈R[|x-y| ≥ |x| - |y|]; where R is the set of real numbers. Proof: Lemma: ∀(x,y)∈R[|x+y| ≤ |x| + |y|] Since x and y are arbitrary real numbers we have, ∀(x,y)∈R[|x+(-y)| ≤ |x| + |-y|] Since |y| =…
R004
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How to solve this equation with 3 unknowns

$$5x-y+3z=3$$$$-3x+y-z=1$$$$-4x+3y+2z=9$$ <=> I take $$3*(-y)+y=-2y$$ and $$3*3z+(-z)=8z$$ and $$3*3+1=10$$third $$4*(-y)+3y=-y$$ and $$4*3z+2z=14z$$ and $$4*3+9=21$$ which results in $$5x-y+3z=3$$$$-2y+8z=10$$$$-y+14z=21$$ and THAT takes away the x…
user1838781
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A question obout the sum of series in $[-\infty,+\infty]$

Suppose that the work set is $[-\infty+\infty]$, we suppose that $$\sum_{n=0}^{+\infty}a_n<+\infty.$$ Now can we says that $$\sum_{n=0}^{+\infty}(a_n-b_n)=\sum_{n=0}^{+\infty}a_n-\sum_{n=0}^{+\infty} b_n\quad$$ In the $[-\infty,+\infty]$ each…
Jack J.
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Parameter solution

Solve the equationsystem $$x+3y+6z=3$$$$x+y+z=-2$$$$-x+y+4z=7$$ if I use Gauss elimination it will be $$x+y+z=-2$$$$3z=9$$$$2y+5z=5$$ and then it will be$$x+y=-5$$$$y=-5$$$$z=3$$ and at the end$$x=0$$$$y=-5$$$$z=3$$ is the parameter…
user1838781
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Failing to complete easy contraposition proof

I struggle a bit with contraposition and would like to know if my approach is right(is my contraposition statement right) I have to show the following statement: If $f(x_0) < \infty$ for some $x_0 > 0$, then $f(x) < \infty$ for all $x > 0$. f is an…
Alex
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Proof verification for linear operators

I gave a proof but it seems rather redundant. What am I doing wrong? Given $A\in F^{n\times n}$ we define an operator $T_A:F^n \rightarrow F^n$ as such: $$T_A(v) = A \cdot v$$ Prove that $A$ is diagonalizable, iff $T_A$ is diagonizable. My…
Alex Osheter
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Can this proof be valid for $\bigcap_{n \in \mathbb{N}}(-1/n,1/n) =\{0\}$?

Assume $∀x, x \in \{0 \}$. Thus $x=0$. So $∀n, x∈(-1/n, 1/n)$ since $0 \in (-1/n, 1/n)$. Hence $$∀n, \{0\} \subset \bigcap_{n \in \mathbb{N}}(-1/n,1/n).$$ Assume $ x \in \bigcap_{n \in ℕ}(-1/n,1/n)$. So $-1/n ≤ x ≤ 1/n$. By Squeezing Theorem, lim $x…
Undergraduate student
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