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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Proving goal having the form $P \lor Q$, is it redundant to separate into two cases?

In Velleman's How to Prove It, the strategy given for proving goal of the form $P \lor Q$ goes like this: If $P$ is true, then clearly $P \lor Q$ is true. Now suppose $P$ is false. [Proof of Q goes here] Thus, $P \lor Q$ is true. I feel like the…
Tan En De
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What a rough proof sketch would look like for a high level software application

Currently I am wondering how to apply proofs to web applications. So far it still isn't clear to me what a proof would look like for such a situation. I would like to see from a math perspective how to write a high level proof for something in the…
user10869858
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Does $\neq$ hold true like $=$ holds true under equation manipulation?

In general, when given some equation with an arbitrary number of variables of the form $$f(a,b,c,...)=g(a,b,c,...)$$ we can manipulate the equation and the equality holds true. For example, we can multiply by constants or variables, subtract…
Hurricane Development
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Show that $(m^2 - n^2, 2mn, m^2 + n^2)$ is a primitive Pythagorean triplet

Show that $(m^2 - n^2, 2mn, m^2 + n^2)$ is a primitive Pythagorean triplet First, I showed that $(m^2 - n^2, 2mn, m^2 + n^2)$ is in fact a Pythagorean triplet. $$\begin{align*} (m^2 - n^2)^2 + (2mn)^2 &= (m^2 + n^2)^2 \\ &= m^4 -2m^2n^2 + n^4 +…
Dave
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induction proof manipulation problem

starting with the LHS, how do you show $(k/30)(k+1)(6k^3+9k^2+k-1)+(k+1)^4$= $(k+1)/30(k+2)(6(k+1)^3+9(k+1)^2+(k+1)-1$ as you can probably tell its part of my induction proof but i cant show this how is it done? thanks Sorry edit its -1 on the end
hitherematey
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Does this count as a proof by structural induction?

Let S be the subset of the set of ordered pairs of integers defined recursively by Basis Step: $(0, 0) \in S$ Recursive Step: If $(a, b) \in S$, then $(a + 2,b + 3) \in S$ and $(a+3,b+2) \in S$. Use structural induction to show that $5 | (a+b)$…
papercuts
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product of odd numbers is odd question

i know how to prove that the product of two odd numbers is odd, but how would i go about proving the other direction... What if i needed to use this as an if and only if statement in a proof, thanks
Carlos Bacca
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Simple proof on set difference

Prove if $A$ is a subset of $B$, then $A\backslash B= \emptyset$. I used a proof by contrapostive. The assumption ($A\backslash B$ not being equal to the empty set) means there exists an $x$ such that $x\in A\backslash B$ implies $x\in A$ and…
Carlos Bacca
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Is this proof on absolute value ok?

Prove that for any real numbers a and b, |a| = |b| if and only if $a^2=b^2$ let $a,b>0$ if |a| = |b| This implies $a=b$ implies $a^2=b^2$ (i then do a similiar thing for $a,b<0$ and when $a<0 , b>0$) let $a,b$ be real numbers if $a^2=b^2$ implies…
jakey22
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$n^2+n$ is even

If $n$ is a positive integer, then $n^2+n$ is even. $n=2k$ for some k in the integers $n^2 +n$ = $4k^2 + 2k$ = $2(2k^2+k)$ as $2k^2+k$ is an integer $n^2+n$ is even. Jst wondering if this proof is ok. AM i allowed to say $2k^2+k$ is an integer?…
Carlos Bacca
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Is this a valid proof strategy?

I was tasked with proving a trig identity -- the particular identity doesn't much matter, as I'm interested far more in whether this is a valid method of proof, generally -- and a professor recommended this strategy: equate both sides and, via dot…
user465188
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Proof of the Sum of Square Roots

I have a question about a problem I encountered: $\exists$ a,b $\epsilon$ $\mathbb{R}$+ such that $\sqrt{a+b}=\sqrt{a}+\sqrt{b}$ Any tips for going about solving this? I tried: $\sqrt{a+b}=\sqrt{a}+\sqrt{b}$ $a+b=a+b$ I have a feeling this isn't a…
K. Barresi
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Smallest digit sum for a specific number

The task of mine is: What is the smallest (non-iterated) digit sum of a positive and natural number that is divisible by $37$? I have already done 80% of the task, I have proven that $1$ can't possibly be true. I also have proven that the digit sum…
calculatormathematical
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Is ''some" equal to "any" in inductive hypothesis?

For example, in proving the following lemma If $n\in\mathbb{N}$ then $n+1=1+n.$ Little gave in his book entitled THE NUMBER SYSTEMS OF ANALYSIS the following proof: Clearly the lemma holds if $n=1.$ Assume as an inductive hypothesis that $n+1=1+n$…
azc
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Prove that if n is an odd integer, then $n^2-1$ is a multiple of 8

I've gotten through proving this all the way to $\cfrac{K^2+K}{8}$, where $n=2K+1$. Since it says that $n^2-1$ is a multiple of 8, the result needs to be an integer, i.e, p (representing $K^2+K$) needs to be something like $2(K^2+K)$. Is using…
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