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.

15776 questions
3
votes
2 answers

Theorem formulation "Given ..., then ..." or "For all ..., ..."?

When formulating a theorem, which of the following forms would be preferred, and why? Or is there another even better formulation? Are there reasons for or against mixing them in one paper? Formulation 0: If $x\in X$, then (expression involving…
equaeghe
  • 185
3
votes
1 answer

Prove: R∩R−1 is symmetric.

The problem that I'm having is proving it - obviously. The only context that I am provided with is: "Prove: R∩R−1 is symmetric." If (x,y) ∈ R then (y,x) ∈ R−1, and since it's the intersection, whatever elements are in the intersection must have both…
Justin
  • 61
3
votes
2 answers

Prove that $ A \subseteq B \iff \mathcal{P}(A) \subseteq \mathcal{P}(B) $.

I'm going through Velleman's How To Prove It and I'm currently on section 3.4 which deals with techniques for proofs involving conjunctions and biconditionals. The title of this question is from one of the exercises. To prove it, I started with a…
MuchToLearn
  • 323
3
votes
1 answer

Proof: Characterize m

Characterize $m$, an integer, such that $m^2≡1 \pmod{5}$. State your characterization as an "if and only if" statement and then prove it. This question is on my study guide for a test that is on Friday (12/5). We are talking about Proof by…
Fallon S.
  • 31
2
votes
2 answers

Prove that $(1+x)^n ≥1+nx$ for all $x>-1$ and $n=1,2,\ldots$

Prove that for every real number $x > −1$ and every $n = 1,2,\ldots,$ $$(1+x)^n ≥1+nx.$$ I don't know where to begin so I haven't tried anything.
user186548
  • 21
2
votes
2 answers

Proof by contradiction how to show is properly

For every $x \in \left[\pi/2,\pi\right]\,,\ \sin\left(x\right) − \cos\left(x\right) \geq 1$. I have drawn the graph and can clearly see that A is true however how do I prove it correctly.
Tk706
  • 271
2
votes
3 answers

Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$

Would this be the same thing as saying "Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for any $s, t \in \mathbb{Z}$"? I can do the proof for any integers $s$ and $t$, but if any and all mean the same thing, then I can do this proof. If not, how can…
JCMcRae
  • 843
2
votes
2 answers

Prove or disprove that if a|(sb+tc) for all (and for some) s,t ∈ ℤ, then a|b, and a|c.

So, this is actually 2 questions in 1. I apologize if that is bad practice, but I didn't want to write 2 questions when they're a word different. So, I have Prove or disprove that if $a|(sb+tc), \forall s,t \in\mathbb{Z}$, then $a|b$, and…
JCMcRae
  • 843
2
votes
2 answers

Induction Proof without Explictly Using The Induction Hypothesis?

I have encountered several problems where one can prove the desired result without actually needing the induction hypothesis. More specifically, you basically just pick $n \in \mathbb{N}$ and run through the argument. In fact, the solution manual…
tchil9
  • 21
2
votes
1 answer

Four-point geometry proof

I'm new to writing proofs and am working with proving finite geometry systems. I'm not sure how I should answer this one. Using the four point finite geometry system: prove that there exists a set of lines in the four point geometry that contains…
Gabby
  • 21
2
votes
2 answers

Basic Properties Explanation

In regards to divisibility I am having trouble wrapping my head around some of the concepts, more specifically some of the general properties of divisibility. for example, why is it possible for x|y, x|z => x|(y-z)? In order to attempt to work this…
Confused_Teacher
  • 21
2
votes
3 answers

Directly prove that $2x^2 -4x + 3 > 0$ for all real $x$

I'm asked (for homework which isn't graded but instead the basis of a quiz) to directly prove that $2x^2 -4x + 3 > 0$ for all real $x$. I am VERY new to proofs. The textbook's only example is a case that was simplified to ( foo )^2 + bar, and it…
Cody Smith
  • 231
2
votes
1 answer

Is this proof by induction correct?

Prove by induction that for all $n\in\mathbb N$, $3\mid n^3+3n^2+2n$. $$P(1) = (1)^3+3(1)^2+2(1) = 6$$ Which is clearly divisble by $3$. Therefore, $P(1)$ is true. Assume $P(1),\ldots,P(n)$ and show $P(n+1)$ is true. $$(n+1)^3+ 3(n+1)^2+ 2(n+1) =…
Vincent
  • 2,329
2
votes
0 answers

Can you share your experience in hand waving and other informal communication regarding mathematical proofs?

I intend to write a paper that will address among other issues the informal communication between mathematicians. My point of origin is the view that every proof can be represented by a sequence of gestalt switches, each described by, sometimes…
Arik
  • 86
2
votes
2 answers

Proving $\gcd(a,p_1p_2)>1$ $\Rightarrow$ $p_1\mid a$ xor $p_2\mid a$ using Euclid's Lemma

Consider the lemma: If $\gcd(a, p_1p_2)>1$, then either $p_1\mid a$ or $p_2\mid a$. How can this be proved using Euclid's Lemma?
user38931
  • 57
1 2 3
…
50 51