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
0
votes
3 answers

Writing formal proof

I need to either prove or disprove that if the square root of n is even, then n is even. I believe the statement is true as there is no such n that contradicts this but I'm not sure about where to start the proof. Thank you.
19515
  • 19
0
votes
2 answers

How can I prove this? For every integer m with 2 divides m and 4 does not divide m, there are no integers x and y that satisfy x^2+3y^2=m.

I know that m is even and m/2 is odd, but I don't know where/how I can use this. Also, 3y^2 is odd and the sum is odd when x^2 is even. I'm trying to prove that its always odd, but I'm stuck. Can someone please help? Thanks
User2345
  • 18
0
votes
1 answer

how to prove the sum of two functions is lower bound of max of two other functions

So I have $4$ functions: $f_1$, $f_2$, $g_1$, $g_2$. I also have in my assumptions that $g_1=\Omega(f_1)$ and $g_2=\Omega(f_2)$. Now I need to prove that $\max(g_1, g_2)=\Omega(f_1+f_2)$. How can this be achieved? Note that my definition of $\Omega$…
dimly_lit_code
  • 7
0
votes
0 answers

Trying out Proof By Induction for First time

I want to show that $(1-r)^x \ge (1-xr)\ \forall x \in \mathbb{N}, r \in \mathbb{R}, 0 \le r \le 1$ This is what I have so far, I'm hoping for a critique as well as help with the end since I don't think I'm quite there yet. Base: LHS =$(1-r)^1 =…
Math1
  • 317
0
votes
1 answer

How can I prove that $a>b $ implies $a^n > b^n$

I am having trouble with understanding this proof $a,b \geq 0$ and a and b are in ordered field How can I prove that $a>b$ $\implies$ ($\forall n \in \mathbb N$ $a^n > b^n$)
gamesn
  • 25
0
votes
0 answers

Is there anywhere to post proofs?

I devised a neat proof that the integral of an odd function over a symmetric interval is $0$. I was immediately tempted to post it to math stack, but feared it would frowned upon as it is not a question. Therefore, I was hoping to find out if there…
infinitylord
  • 4,777
0
votes
1 answer

Is this good enough of a proof? (I know almost nothing about proofs)

The homework question is "Prove that if and are rational numbers then 2 + 3 is a rational number" So I wrote this to try to prove it: *Let r and s be rational numbers By definition of rational, r = a/b and s = c/d and a, b, c, and d are integers…
davidib17
  • 25
0
votes
1 answer

Expanding Proof by Elimination

For proof by elimination, if I have $A$ implies $B$ or $C$: $A \Rightarrow (B \vee C)$, then I need to show if $A$ and $\neg B$, then C. What happens though, when we have $A$ implies $B$, or $C$, or $D$: $A \Rightarrow (B \vee C \vee D...)$ and so…
Math1
  • 317
0
votes
1 answer

How to get started on this proving this set?

Let $R$ denote the set of all round integers and let $S$ denote the set of strange integers. Show that $R \cup S = \mathbb{Z}$. An integer $n$ is called strange iff there exist an integer $k$ such that $n=3k+1$. An integer $n$ is called round iff…
ash
  • 99
0
votes
1 answer

How could I prove/disprove that there is a function with outputs equal to a function of one higher degree for all natural numbers

So, I'm wondering if the relationship $$x^n=a_1x^{n-1}+a_2x^{n-2}+...+a_{n-1}x+a_n$$ exists, where the value of the left and right side are equal for all integer values of x greater than zero up to the integer n. I am looking for being able to find…
Will Johnson
  • 13
0
votes
0 answers

Let $S=${$a^2+b^2: a,b\in\mathbb{N}$}. Prove that $S$ is closed under multiplication.

Let $S=${$a^2+b^2: a,b\in\mathbb{N}$}. Prove that $S$ is closed under multiplication. Proof trying. Let $a_{1},a_{2},b_{1},b_{2}$ in $\mathbb{N}$. We will show that $\left( a_{1}^{2}+b_{1}^{2}\right) \left( a_{2}^{2}+b_{2}^{2}\right) \in S$. So, …
user295645
0
votes
0 answers

Proof by induction, inductive step built from hypothesis

Suppose we are trying to prove some $P(n)$ by using proof by induction First we show that $P(0)$ is true Then we assume that $P(n-1)$ is true In practically every math proof I have seen, in the inductive step we start with $P(n)$ and break it into…
Jason
  • 3,563
0
votes
1 answer

Let $n$ be a positive integer. Prove that if $n^{5}-1$ is prime then $n=2$.

I should show $n^{5}-1= (n-1) \left( n^{4}+n^{3}+n^{2}+n+1\right)$ prime. So, how? Proof trying. We know $\left( n^{4}+n^{3}+n^{2}+n+1\right)$ is odd.
user295645
0
votes
1 answer

Let $a$ and $b$ be real numbers. Then $\left( a+b\right) ^{3}=a^{3}+b^{3}$ implies $a=0$ or $b=0$.

My proof. We need to show that $a=0$ or $b=0$ for the equation. We have, $\left( a+b\right) ^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}$ (by the binomial theorem) $=a^{3}+b^{3}$ (by the assumption). Now, adding $(-(a^{3}+b^{3})$ both sides yields…
user295645
0
votes
2 answers

Use induction to prove the Division Algorithm?

So I am trying to Prove the division algorithm by induction. The Division Algorithm is written in my book as this: The Divison Algorithm for Natural Numbers If $n$, $m$ are natural numbers and $n\leq m$, then either There is a natural number…
Christian Soto
  • 1
1 2 3
…
50 51