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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Prove or Disprove: Subspaces, and Bases

Prove or disprove: If U is a subspace of a finite dimensional vector space V and B = {v1, . . . ,vn} is a basis for V, then some subset of B is a basis for U. So far, I don't know where to start. I could assume that since B is a basis, it is…
Ian Murphy
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Find a basis given a vector space

The following question is what I want to solve: Given that V = ${(a,b)}$ is a vector space, and addition is defined as $(a,b) + (c,d)$ = $(a + c - 1, b + d)$, and multiplication is defined as $r • (a,b)$ = $(ra - r + 1, rb)$. Find a basis for V. So…
Ian Murphy
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Prove formulae using natural style

Prove: $((P ⇒ R) ∧ (Q ⇒ R)) ⇔ ((P ∨ Q) ⇒ R)$ Notation: $P[x]$ and $f[x$] for “$P$ applied to $x$” and “$f$ applied to $x$”, instead of $P(x)$ and $f(x)$. So far I tried the following: Direction $=>$ Assume ( (P => R)^ (Q => R) ) (1) and Prove (…
Contourette.
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How to find all the equivalence classes for a specific equivalence relation?

What are the equivalence classes of the following equivalence relation $$S=\{(x,y) \in \mathbb{R} \times \mathbb{R} \mid x - y \in \mathbb{Q} \}$$? I know that an equivalence relation $R$ on a set $A$ induces a partition $P$ on that set. This…
user168764
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$S$ is a reflexive closure of $R$. Prove that if $R$ is symmetric, then so is $S$

Suppose $R$ is a relation on $A$, and let $S$ be the reflexive closure of $R$. Prove that if $R$ is symmetric, then so is $S$. S is the reflexive closure of $R$, which means that $$\forall x \in A (x, x) \in S$$ This is nice. Now, I assume $R$…
user168764
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Prove an x exists with f(x) = f(x + T/2)

Suppose $f: \mathbb{R} → \mathbb{R}$ is a continuous and periodic function with period $T > 0$. Show that: there exists an $x \in \mathbb{R}$ such that $f(x) = f(x + T/2)$. We figured out we needed to use the intermediate value theorem (our…
Tiamo P.
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Writing mathematical proof

i have just finished Multivariate calculus and so far all the mathematics i have done are those calculations sort of questions. However i began to realize that it is not the proper way to do maths and i wanted to learn maths rigorously by proving…
Huiying
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How to prove/disprove proof on limits (delta-epsilon)

Prove or disprove: $$ \forall \epsilon > 0, \exists \delta>0, \forall x, y \in \mathbb{R}^+, |x - y| > \delta ⇒ |x + y| > \epsilon $$ I've been trying this for some time now but can't seem to get anywhere. I tried proving it then disproving it. Need…
yus_m
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Proving quadratic inequalities?

I am trying to prove that $$e^{k+1} ≥ 3 + 3k + k^2$$ with, $$k>2$$ WhatI have done so far: What we are trying to prove is that $$e^n≥1+n+n^2$$ is a true statement. Since $n=3$ holds, this is our base case. Then, the inductive hypothesis is:…
Lerbi
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Set difference bijection proof (stuck on injective)

So here is the question I'm working on So obviously I need to prove two things, that its both injective and surjective, however I'm trying to show it is injective and am currently stuck, here is what I have As you can see, double containment to show…
k9b
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Positive convergence of terms proof

Let $(s_n)$ be a sequence of positive terms such that the sequences of ratios $(\frac{s_n+1}{s_n})$ converges to $L$. Prove that if $L>1$, then $\lim s_n=+\infty \!\,$ So I know I have to use the theorem in my book that says "let $(s_n)$ be a…
Math Major
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Need help proving a surjection / uncountability

Here is what I think. A) To prove a surjection.. it goes like this. Take an arbitrary b in the Real Numbers (codomain). Let a = "SOMETHING" and we want to show f(a) = b. Now since the function is defined by F(x,y) = x and b is in the real numbers.…
k9b
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Prove: For any integer $n \geq 2$, there is an odd number P such that $2n \lt P \lt 3n$

I am in high school and had this for a homework problem. I got it wrong, but the teacher did not post the correct answer. Any help would be appreciated. It is about writing proofs. Prove that for any integer n greater than or equal to 2, there is…
Brenda
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Cardinality with Cartesian Cross Product problem

A and B are finite sets Prove that |AxB| = |A||B|. I need a solution/hint. I suspect that the answer has to do with the fact that the we can say that |A| = |B| and then from that say = |AxB|. I think I have a solution for it, but I just wanted to…
k9b
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Writing clear proofs involving multiple theorems and conditions

Suppose the problem is that given $A$ and $C$ holds, prove $D$ holds. Some theorems that we can use are: $A \to B$ $(B,C) \to D$ I feel what I said may be unclear: Because $A$ holds and $A$ implies $B$, $B$ holds. Because $B$ and $C$ holds and…
Tim
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