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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simple proof algebra question on' or'

If $x^2+5y=y^2+5x$ then $x=y$ or $x+y=5$, where $x$ and $y$ are real numbers . Prove this statement. Can someone help me with this problem or how to approach it? I can get x=y Does this mean i have proved the statement because it is an 'or'? Thanks
Harry
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induction question understanding

Im wondering if this template for induction would be valid show true for n=1 assume true for n=k Attempt to show true for n=k+1 but at this point just replace n with k+1 and dont use the assumption that n=k. show that the expression with n replaced…
hitherematey
  • 105
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understanding proof by contradiction

Below is not a completed proof but a logical structure i am unsure of. Given line 1, i do not understand line 2. I would understand it if it were: The case when $m=p_1n+r_1=p_2n+r_2$ and $r_1\ne r_2$ and $p_1=p_2$ implies a contradiction that…
hitherematey
  • 105
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A proof involving inequality

Let $x$ be any real number such that $x^2-3x+2<0$ then $1
Carlos Bacca
  • 638
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Simple proof involving integers

Does this look ok to you? let $m, n$ be any integers and $mn$ and $m + n$ are both even, prove that $m$ and $n$ are both even. So $mn$ and $m+n$ are integers from what we are given we can assume even integers. $mn+m+n=2(j+p)$ for some $j$ and $p$ in…
hitherematey
  • 105
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2 answers

help proving statement with quantifiers and inequalities

I need help with the following: Prove that for any $y$ in $\mathbb{R}$, there exists an $x$ in $\mathbb{R}$ such that $x-7>3y$. I tried to approach it by contradiction, leaving “there exists a $y$ such that for any $x$ such that $x-7\leq 3y$, though…
J--
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question on proof method

if you proving someting like if a relation is symetric. say R is a relation on Z and $xRy$ if x+y is a multiple of 3. Then you want to prove symetry and say for some $x,y$ in Z $xRy$ if $x+y=3k$ k some integer This implies $y+x=3k$ $yRx$ so $R$ is…
Carlos Bacca
  • 638
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The 'formal' way to prove equivalence?

In school we were always taught to prove equivalence by splitting an equation into $LHS$ and $RHS$ and working with each side individually until $LHS = RHS$. For example, prove: $$2^{k + 1} - 2 = 2(2^k - 1)$$ Which could be done as follows: $$RHS =…
Xenon
  • 259
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proof on equality of sets

If i want to Prove $A^c \cup B^c$ = $(A \cap B)^c$ by a string of equalities =$\{x|x\in A^c \cup B^c\}$ =$\{x|x\in A^c orx\in B^c\}$ =$\{x|x\notin A orx\notin B\}$ =$\{x|x\notin (A \cap B)\}$ =$\{x|x\in (A \cap B)^c\}$ 1/ Is this proof ok as it…
Carlos Bacca
  • 638
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How does one select some $i$ to prove $\exists i$ s.t. $s_i \leq A$ where $A$ is the average of real numbers $(s_1 + s_2 + . . . + s_n) / n$

How does one select some $i$ to prove $\exists i$ s.t. $s_i \leq A$ where $A$ is the average of real numbers $(s_1 + s_2 + . . . + s_n) / n$ It seems like a trivial proof, but writing a proof for such an existence conventionally does not seem…
Leonardo
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proof involving double complement

Prove $(A^c)^c$ = $A$ $(A^c)^c = \{x|x\in (A^c)^c\}$ $(A^c)^c = \{x|x\notin A^c\}$ by definition of complement $(A^c)^c = \{x|\ (x \in A)\}$ by definition of complement Therefore $(A^c)^c=A$ Is this proof ok, I'm not sure if its valid? thanks
Carlos Bacca
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How to prove $\sum_{I=1}a_{I}^{2}$ is larger than $\frac{1}{n}$

How to prove $\sum_{I=1}^{n}a_{I}^{2}$ given constraints that $\sum_{I=1}^{n}a_{I}$ = 1 is larger than or equal to $\sum_{I=1}^{n}(\frac{1}{n})^{2}$?
Song Calderone Zhang
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(very) simple proof of sets

If you have two very simple sets $\{1,2\}$ and $\{2,1\}$ and you want to prove they are equal can you just say they are equal by definition and a simple observastion? Thanks
Carlos Bacca
  • 638
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When is it more appropriate to describe steps using English rather than mathematics?

For example, are there set cases when one would write "$x$ is a positive integer" instead of writing "$x \in \mathbb{Z}^{+}$", or vice versa?
VortixDev
  • 181
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Multiplicative Inverse Proof

If x and y are real numbers, then $\left ( xy \right )^{-1}$ =$x^{-1}y^{-1}$. I'm not quite sure where to start on this proof since $\left ( xy \right )^{-1}$ will only exist if xy $\neq 0$. If I start the proof there, then I'd have two cases; case…
Jan
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