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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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Prove factorial?

$k! > \frac{k}{2}^\frac{k}{2} \text{ for } k\in N$ I'm not sure how to prove this, is it valid to rewrite it as?: $(2k)! > k^k \text{ for } k\in N$ Edit: I think I proved it... $(2k)!=1\cdot2...k\cdot(k+1)...(k+k)>k!k^k$ $(2k)!>k!k^k>k^k$
user1768788
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What is the difference between the hypotheses of these two mathematical statements?

I am unable to understand the difference between the hypotheses of the following two mathematical statements. Example 1: The sum of the first $n$ positive integers is $n \dfrac{ (n + 1) }{ 2 } $ Hypothesis: $n$ is a positive integer. (Note that…
The Pointer
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Proofs of sets and subsets and inverse

There is an assignment which I need to complete for school and I have absolutely no clue on how to solve the following question. If A and B are sets and $f: A \rightarrow B$, then for any subset $S$ of $A$ we define $f(S) = \{ b \in B:b = f(a)$ for…
Jake0991
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How would I go about to prove this?

$n\in \{0,1,2,3,4,5,6,7,8,9\}$ Prove that $n$ is evenly divided by $5$ only if $n$ is $5$ or $0$. Only way I could think of proving it would be repeat like this: $0\mod 5 = 0$ $1\mod 5 = 1$ etc... But it doesn't feel acceptable.
user1768788
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Is this a valid deductive proof of $2^x \geq x^2$ for all $x \geq 4$?

I saw a video of somebody saying that you can prove this by saying that $x+1$ will grow by $2$ on the LHS and by $(x+1)^{2}/x^{2}$ on the RHS. But I am not convinced that this is a clean deductive proof. Do you agree and if so, how can one make a…
Wuschelbeutel Kartoffelhuhn
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$|a-b|

For $a,b\in\Bbb R$ prove $|a-b|
user374968
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Is this reasoning in this type of proof writing correct?

So Im encountering some excercises of the type: Let $G$ be a finite group and $S,T$ non empty subsets not necessairily distinct. Show that $ST=G$ or $|G| \geq |T|+|S|$ So in general I try to prove this in the following way: I start by saying, if…
Joaquin Liniado
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Prove that the set of positive rational values that are less than $ \sqrt{2}$ has no maximum value

Its been a while since I've written a proof and would appreciate some feedback on this one. Question: Given the set of rational positive values, $\{q | q \in \mathbb{Q} \wedge 0 \lt q \lt \sqrt{2}\}$, show that there is no maximum value for $q \lt…
Jason
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cutting a string at positions ids in any order yields same set of chunks

Cutting a string at 'n' positions in any order will yield same cut pieces. Is there any standard mathematical proof which supports this ? For example say "elephantsinforest" is the string. Cutting the string at id cut positions in increasing order…
ganapathi
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Examples of xkcd's magic proofs

Today's xkcd describes magic proofs. Can anyone think of some good examples of these?
kdog
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Can I write proof this way?

So I have written a solution to a simple problem and it is as follows: Let $E_{1}$ denote dealer gets a black jack and $E_{2}$ denote that the player get a blackjack. Note that there are $\binom{52}{2,2,48}$ outcomes in total, and…
Mathemagician
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How to proove that a set containing the smallest element is also globally the smallest set?

I have a set, $$ X = \{ x_1, x_2, x_3, \dotsc, x_n \}~. $$ The elements $x_i$ from this set are the input to a combinatorial problem I solve with an algorithm. The algorithm returns a solution set, $S \subseteq X$. However, there are usually more…
Technaton
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What statements to write for using proof by cases in a proof by contradiction?

In a theorem that I am trying to prove I first use proof by contradiction and for reaching contradiction I need to prove using cases. Now for formally writing proof by contradiction we use the following structure - Method: In order to prove a…
Joy Chopra
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How can I prove $\frac{m+a}{m+a+l+b}$ is between $\frac{m}{m+l}$ and $\frac{a}{a+b}$?

Let $m,a,l,b \in \mathbb{Z}^{+}$ How can I prove $\frac{m+a}{m+a+l+b}$ is between $\frac{m}{m+l}$ and $\frac{a}{a+b}$?
user308485
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Proof that $A + 1 \leq e^A$ for all $A > 0$

I was reading a proof where at a certain point the prover uses the following inequality $$A + 1 \leq e^A$$ which in my opinion needs also a proof to be used around. I think I'm missing some important fundamental property which is well-known, but I'm…
user168764
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