Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [proof-writing]

For questions about the formulation of a proof. This tag should not be the only tag for a question and should not be used to ask for a proof of a statement.

Questions with this tag are about the presentation of a mathematical proof. Questions might include:

  • Should I include [x-mathematical detail] at [y-part of this proof]?
  • Is the following a sufficient proof of [x-mathematical tidbit]?
  • I have written the following proof, could I somehow improve it, does it have good flow/can I improve readability?

But this tag is not for asking someone else to write a proof for you, or for how to answer some question. Questions such as: My professor asked me to prove the Pythagorean theorem and I don't know how to begin are not to have this tag.

This tag is intended for use along with other, more "mathematical" tags. A question about the writing of a proof in abstract algebra, for example, should have as well. This tag can be used along with the proof verification tag.

See here for a useful set of guidelines for writing a solution.

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To show that there is no $l$ that satisfies a certain property.

Let $f \in C[a,b]$ define $\|f\| _{1} =\int_{a}^{b} |f|.$ (b)Show that there is no number $l$ such that$\|f\|_{\max} \leq l \|f\| _{1}, \forall f \in C[a,b].$ Could anyone help me, please?
Emptymind
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Help with an inequality proof

Write Taylor polynomial of degree 3 for $f(x)=\cos x$ at $a=0$, and prove that $$0 \leq E_3(x) \leq \frac{x^4}{24}$$ This is what I have done so far. I struggle mainly with the right side of the inequality. $E_3(x)=f(x)-P_3(x)$ $f(x)=\cos…
Mathomat55
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Proving given sets are mathematical intervals

Let’s assume we have a subset of real numbers called $S$. We call the set of upper bounds of $S$, $U$ and we call its set of lower bounds, $L$. If we define a set called $G$ that consists of any real number not included in the sets $S$, $U$ and…
Jigsaw
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Have you ever encountered this kind of proof

Have you ever encoutered a proof like this one : If $Q$ is true then $P$ is true. If $Q$ is false then $P$ is true. Therefore $P$ is true.
LIR
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√7 is irrational. how to prove it

(√7) is (IR) irrational Number. How to prove it√7 . Firstly I tried a/b =√7 and a^2 /b^2 =7 7b^2=a^2 And then I couldn't continue . How I can Prove it ?
David
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Prove the mean value of some binomial distribution??

Hello I am just baffled on what to do to derive or begin this question. My futile attempt was to let N approach infinity (b/c after infinite trials the mean should reach to Np under assumption) and see if there were any patterns or cancelations…
CuriousJ
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Can I prove a numerical inequality by manipulating it and ending at a true statement?

Say I want to prove that $\sqrt2$+$\sqrt3$ < $\sqrt10$. The steps I would do to prove this is square both sides to get: 5+2$\sqrt6$<10 (subtract 5 from both sides): 2$\sqrt6$<5 (square both sides): 24<25 which is true. but does this constitute as…
Harold Smith
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Proof using method of contradiction. Use the method of contradiction to prove that √2 is irrational.

Use the method of contradiction to prove that √2 is irrational. I don't understand how to prove that √2 is irrational using this method. And I feel difficult to form the contradiction.
vestika weerachandra
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How to show the equivalence of two hyperplane representations?

I have the following equivalent representations for a hyperplane: $H:=\{x\in\mathbb{R}^n\vert w^T\cdot x=d\},\quad w\in\mathbb{R}^n,d\in\mathbb{R}$ fixed and $H_2=\left\{x_0+\sum_{i=1}^{n-1}\lambda_i…
baxbear
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Show that if f is strictly increasing on A, then inverse f is strictly increasing on B

Let A, B ⊆ R, and let f : A → B be a bijective function. Show that if $f$ is strictly increasing on A, then $f^{-1}$ is strictly increasing on B. How would I write this proof? I think by contradiction but I don't know where to start.
badieshisha
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How to mathematically define a set generated from $n$ numbers in a generalized manner (to be used in a proof for an arbitrary size)?

This is what I mean: I have three numbers $[a,b,c]$ and I can produce a set from the numbers comprised of pairs of $1$ number and the sum of the other two numbers, ie. $\{(a, b+c), (b, a+c), (c, a+b)\}$. With four numbers $[a,b,c,d]$, the set…
JPrince
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Proof by contradiction on if and only if statements

Suppose I want to prove a general statement like 'A is true if and only if B is true' If I assumed B is untrue and showed that subsequently A is untrue, which direction am I actually proving? I guess it is the direction going from left to right?
UnsinkableSam
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Question about how to approach existence in proofs

I am working through some problems in Axler's Linear Algebra Done Right textbook, and I noticed that I haven't really developed an intuitive feel for how to approach existence in the proofs. The idea of existence just seems very vague to me. For…
Richard K Yu
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Basic negation of a statement

Statement is $\exists I = (x_o - \frac{1}{n}, x_o + \frac{1}{n}), n \in \mathbb N$, s.t $f(x) > 0 $ $\forall x \in I$ When negating the part after "such that", would it be $f(x) \leq 0$ $\forall x \in I $ or $\exists x \in I$ s.t $f(x) \leq 0$ ?
MinYoung Kim
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