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
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How to prove that $4x \le x^2 + 8$ for all $x$

I need to find a way to prove the above statement, and feel that doing it by individual cases is not the best method.
Udyr
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Prove the following using induction

$$\frac{1}{1*2} + \frac{1}{2*3} + ... + \frac{1}{n(n+1)} = 1 - \frac{1}{n+1}$$ I'm new to induction, but this is what I cam up with so far. $$1 - \frac{1}{k(k+1)} + \frac{1}{(k+1)(k+2)} = 1 - \frac{1}{k+2}$$ $$1 - \frac{k+2+k}{k(k+1)(k+2)} = 1 -…
Tom Stanton
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Prove A bijection is increasing on it's inverse as well as the original function

Let $f:A \rightarrow B$ be a bijection, where $A$ and $B$ are subsets of $\mathbb{R}$. Prove that if $f$ is increasing on $A$, then $f^{-1}$ is increasing on $B$. I have an idea of the picture of how this is true, but I don't know how to prove this…
hawk2015
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Proving with well-ordering principle

I have this conjecture: Let a and b be integers and n and m natural numbers. $$ a \equiv b \bmod n \Rightarrow a^m \equiv b^m \bmod n$$ I think I got the induction proof, but I'm having difficulties on how to proof this with well-ordering…
dendritic
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How to write down this simple proof? (in natural numbers, if for every number there is a smaller number then 1 is in the set)

This seems undeniably true to me, but I don't know how to write it down. Given the non-empty set $S$ containing only natural numbers (starting at 1, not 0). If for every number $x$ greater than 1 there is a number $y$ such that $y
Lara
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Proof that $ab/(a+c)$ is bounded for bounded $b$ and $c$

Is there a concise way to prove that $\frac{ab}{a+c} \in [0, 1]$ for all $a > 0$, $b \in [0, 1]$, and $c \in [0, 1]$?
ezod
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Can someone help me give a proof for this?

I know there are theorems about integrals of odd and even functions, but i kept wondering about integrals that share symmetry around an axis $x=c$. I've been trying to give a proof for this but can't seem to get around it; could someone help me…
zickens
  • 316
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How to prove that the cross product of a countable and uncountable set is uncountable?

so my question is, how can you prove that ${\Bbb Z}$ x ${\Bbb R}$ is uncountable? So far I have tried proving that there is an uncountable subset of ${\Bbb Z}$ x ${\Bbb R}$ without luck and I'm not really sure what I can do Thanks for any tips…
Rdewolfe
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Proving the well ordering principle

THe well ordering principle has that every subset of $\mathbb{Z}^+_0$ has a least element. or if $S$ is a non-empty subset of $\mathbb{Z}^+_0$ and $S = \{a_1, a_2, a_3 ... a_n\}$, then there is a least element (say $a_1$) which is lesser than $a_2,…
Max Payne
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Contradiction proofs

I'm a first year Physics student and I have some trouble approaching Proofs by Contradiction in some of my Math classes. Once I get the first 2 or 3 statements I can finish the proof but a lot of the time I can't immediately get the first step. Any…
Sreekar Voleti
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Developing proof writing and logical skills

What resources can a person turn to in order to develop their proof writing and logical skills? The advanced calculus course I'm taking has made me realize how weak my logic and proof writing skills are, I'm struggling to write even basic set…
Stacks of overflow
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Proving existence of a unique real number

I am working on the following question: For all $x \in \mathbb{R}$, $x \neq 6$, there exists a unique real number $y$ such that $xy+x=6y$. Now I have the existence part. That there exists a $$y=\frac{x}{6-x}.$$ To show uniqueness I know that I must…
Vasi
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What should I learn to increase my skill to find proof?

I know... reading lot of proofs and comments about them and working hard by myself on proving theorems are probably the only good solutions. But in the same time, it is not a solution at all because If I'm stock or if I only manipulate formulas…
jvtrudel
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Proof by exhaustion: all positive integral powers of two end in 2, 4, 6 or 8

While learning about various forms of mathematical proofs, my teacher presented an example question suitable for proof by exhaustion: Prove that all $2^n$ end in 2, 4, 6 or 8 ($n\in\mathbb{Z},n>0$) I have made an attempt at proving this, but I…
Delan Azabani
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how to prove the uniqueness and existence of equations

I've the equation $e^x=5$, know it has the solution $x=\ln 5$. How to prove the existence before, and after the uniqueness of this solution?
Jianluca
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