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
5
votes
2 answers

Prove the Correctness of Horner's Method for Evaluating a Polynomial

I am currently studying the Skiena `Algorithm Design Manual' and need a little help with a proof of correctness. The problem goes as follows: Prove the correctness of the following algorithm for evaluating a polynomial. …
semicolon
  • 51
5
votes
1 answer

Symbol for "by the definition of"

I find that I am using the term "by the definition of" a lot in my proofs, especially after && in align* environments. Is there a symbol that I can use instead for conciseness? Example: Having established that $x$ is odd, I would say $x=2k+1$ for…
Murey Tasroc
  • 403
5
votes
4 answers

Considering sets in proofs

In order to show that $\forall x\gt0, \ \exists n_0\in \mathbb N: \ n_0(n_0+1)\le x\lt (n_0+1)(n_0+2)$, the proof in my textbook considers the set $A=\{n\in \mathbb N :n(n+1)\le x\}$ and then goes to show that $A$ has a maximal element $n_0$, which…
fuzzypixelz
  • 674
5
votes
1 answer

Prove that $f(n) \geq n$

Let $f$ be a function from $\mathbb{N}$ to $ \mathbb{N}$ such that $\forall n \in \mathbb{N}$, $f(f(n))
Noctisdark
  • 383
4
votes
3 answers

Direct proof and contradicttion

If a statement has direct proof, it can not be proved by contradiction. Is it true? I want to know if a question has direct proof: can we once again prove by contradiction method too?
gourija
  • 41
  • 1
4
votes
3 answers

What is the relation A = B = C called in a proof?

When writing a proof if I have the relationship $$ A = B = C $$ And I want to use that to prove $$ A = C $$ I remember there being some term for it. What is that term, and what would be an appropriate intertext in this situation?
jsj
  • 535
4
votes
2 answers

Is this proof of big O correct?

Show that $n^2 -10\notin O(n)$ My friend keeps on insisting that my proof is incorrect. Could you please tell me if there is a mistake? (made suggested edit) Proof: Suppose to the contrary that $n^2 -10\in O(n)$. By definition this means there…
Mark
  • 3,109
4
votes
2 answers

Formatting for problem sets?

What is considered a good format for writing problem sets in mathematics? Are there any good examples of problem sets that are well-written and formatted that you can show me?
okarin
  • 2,221
  • 1
  • 21
  • 42
4
votes
2 answers

learning how to write proofs properly

I am learning how to structure my proofs in such a way that others can read them with ease. It was pointed out to me several times on this site that my proofs are not very clear. Anyway, here goes: The number r is rational iff -r is…
Adam
  • 3,422
  • 1
  • 33
  • 50
4
votes
3 answers

Give an infinite collection of intervals such that $A_{n+1} \subset A_n$ and $\cap^{\infty}_{n=1} A_n = \varnothing$

Give an example of an infinite collection $A_n $ of intervals such that $A_{n+1} \subset A_n$ and $\bigcap^{\infty}_{n=1} A_n = \varnothing$. I have come to the following collection of intervals, but dont know if it is correct nor how to prove it.…
user1090614
  • 427
4
votes
4 answers

Low Level Well-Ordering Principle Proof

Suppose that I have k envelopes, numbered $0,1,...,k−1$, such that envelope i contains $2^i$ dollars. Using the well-ordering principle, prove the following claim. Claim: for any integer $0 ≤ n < 2^k$, there is a set of envelopes that contain…
Sonny Gasson
  • 43
4
votes
1 answer

common mistakes with induction proofs specifically inequalities

I have a question involving a tempting method when proving the statement: $2^{n}>n^{2},$ for $n \geq 5.$ basis step: we can show that when $n=5,$ LHS: 32, RHS: 25, so our base case holds. Induction hypothesis: let us assume that: $2^{k}>k^{2},$ is…
string_orbifold_iib
  • 47
  • 2
4
votes
7 answers

Structure of a proof by contradiction

I know this is a trivial question, but it has been bothering me for a while. My textbook says "Proof of contradiction exploits the fact that the statement "if A holds, then B holds" is equivalent to the statement "if B does not hold, then A does not…
T. B.
  • 71
4
votes
3 answers

How are proofs normally constructed in a write up, in one line or split up into multiple lines?

Here is the same proof formatted two different ways. My questions is what is the standard for a writeup like a homework assignment? I think the first one looks better but I don't think that is the way that I normally see it. If someone could just…
Jac Frall
  • 775
4
votes
2 answers

How did Hardy make this step in proving two surds are dissimilar if they are non-perfect square integers with no common factor

Overview I am attempting to replicate a proof Hardy provided in his book - A Course of Pure Mathematics, yet am having trouble with one of the steps. I was wondering if someone can explain how he made a step in the proof. Statement If $M$ and $N$…
GovEcon
  • 2,656
1 2
3
…
50 51