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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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Confusion regarding assumption

https://proofwiki.org/wiki/Mean_Value_Theorem This isn't a question about the Mean Value Theorem per se, but about something in the first proof. There is this line towards the beginning of the proof: F(x) = f(x) + hx, which the previous line says is…
Sayan Sarkar
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The use of the terms 'weaker' and 'stronger' in theorems and assumptions

This may be a basic question, but I'm not a native English speaker. So I just wanted to obtain clarification on something: A theorem is weaker resp. stronger if the assumptions/conditions needed to prove the theorem are stronger resp. weaker. Is…
Frido
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How many steps do you have to show when evaluating an equation in a proof?

In a proof like this: It just goes from a complicated looking expression into just $x$, is that allowed? What are the rules for this?
enoopreuse22
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What does the absolute value of substituting a point (not lying on a line) into a line means

I am not sure mathematically, if my understanding to $|Ax_p+By_p+C|$ to be correct. I noticed in a code that it is being used as a kind of distance of a point $P=(x_p,y_p)$ to line L $Ax+By+C = 0$ For that I am asking the question, what is the…
Mour_Ka
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Can a corollary depend on another corollary?

Is it good or bad practice to have a corollary depend heavily on another corollary? An alternative approach would be to state one of the corollarys as a theorem.
Limmen
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Prove that a homogeneous function is either concave, or convex

I need to prove that every homogeneous function on the domain of all positive real numbers is either concave, or convex. UPD Let f(x) — homogeneous of degree k, then f(ax)=a^kf(x). Then, for x1,x2>0 and a within the interval [0,1], f(ax1)=a^k*f(x1)…
Ksenia
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How do you prove a chain of implications?

$\newcommand{\Ra}{\Rightarrow} \newcommand{\Q}{\mathbb{Q}}$ We prove $P \Ra R$ by assuming $P$ then showing some middle $Q$, i. e., $P \Ra Q \Ra R$. What if we have to show $A \Ra B \Ra C$. Do we prove this one implication at a time, say, Assume $A$…
scribe
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How to prove exactly one conclusion holds

Let's say we're given two conclusions A and B and we want to show that only one can be true at once. Can I prove this by assuming A and showing that B cannot be true and vice versa?
mathnerd
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Proof By Contradiction Divisibility Question

Use prove by contradiction to prove that for all integers p , q and r, if p is not divisible by qr then p is not divisible by q
Dexter Tan
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How to include in a proof the probability of something happening?

I was attempting to prove a statement in which I want to include that if some condition doesn't hold, then there is a a setting in which we would get a contradiction. I realise this is not a good way to phrase the question, so maybe a specific…
Seeker
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How to alleviate this ambiguity in the placement of implicit universal quantifiers? (Long).

Here's an example of a general problem I have sometimes. As an example, lets take the theory of prosets (aka 'pre-ordered' sets). We begin with a transitive and reflexive relation $\leq$, and we extend our theory with new definitions which we can…
goblin GONE
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Let $f$ be a function such that $f(xy)=xf(y)+yf(x)$ for all $x,y \in \mathbb{R}$. Prove that $f(1)=0$ and that $f(u^n)=nu^{n-1}f(u)$

$u \in \mathbb{R}$ and $n \in \mathbb{N}$. To prove that $f(1)=0$, am I on the right track by letting $x=\frac{1}{y}$ to get $f(xy)=f(\frac{1}{y}y)=\frac{1}{y}f(y)+yf(\frac{1}{y})$? If yes, how do I get $0$ from that? To prove…
cypherfry
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Let $x$ be a fixed real number. Prove: if $x^5 + 2x^3 + x < 50$, then $x < 2$

This is the problem: Let $x$ be a fixed real number. Prove: if $x^5 + 2x^3 + x < 50$, then $x < 2$. It's from the book "An introduction to mathematical proofs" by Nicholas A. Loehr. I tried to prove it using a direct proof and then trying to prove…
David
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Proving/Disproving the Converse of the First Derivative Test

The First Derivative Test says that the function f is continuous on [a,b] and differentiable on (a,b), except possibly at c in (a,b). a) We can prove that if f ' (x) > 0 for x in (a,c), and f ' (x) < 0 for x in (c,b), then f has a relative maximum…
k_math
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Prove For any $k\in \Bbb R,$for any $n\in \Bbb N$ \ {$0$} ,there exists some $z\in \Bbb C$ such that $k^2+n\lt |z|$.

$(A):$For any $k\in \Bbb R,$for any $n\in \Bbb N$ \ {$0$} ,there exists some $z\in \Bbb C$ such that $k^2+n\lt |z|$. $(B):$For any $n\in \Bbb N$ \ {$0$},there exists some $z\in \Bbb C$ such that for any $k\in \Bbb R,k^2+n\lt |z| $. The first part of…
sunny
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