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.

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Demonstration of strong induction using ladder rungs

My textbook illustrates strong induction using a ladder analogy as follows: Suppose we can reach the first and second rungs of an infinite ladder, and we know that if we can reach a rung, we can reach two rungs higher. Prove we can reach every…
yroc
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Use division algorithm and then induction to show 3|(n³+2n) for all ℕ.

For division algorithm, would I do something along the lines of n³+2n = 3q+r and go from there? For induction, I did the base case, which is true, and so then I moved on to the k+1 case, in which I did (n+1)³ + 2(n+1) to get n³+3n²+5n+3, which isn't…
JCMcRae
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Suppose that x is an integer. Use a proof by contrapositive to prove that if 5x+7 is even, then x is odd.

I know that we assume x is even. So, as x is even, x = 2k for some integer k. Then, that would make for 5(2k)+7 = 10k + 7. And this is where I'm stuck. I know that it isn't complete at 10k+7 to prove that it is odd, but I do not have a clue as to…
JCMcRae
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Need help proving the statement

Assume that D ⊂ N and D ̸= ∅. Prove or disprove using a detailed structured proof, justifying every step: [∀x ∈ D, ∃y ∈ N, y < x] ⇔ [0 ̸∈ D] I have no idea how to prove a statement like that, I'm completely stuck! If anyone could help me out in any…
Guestt
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If a tree has order 2 or more, then the minimum cut set is 1.

Prove: If a tree has order 2 or more, then the minimum cut set is 1.
Vincent
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Mathematical proofs with Cardinality

Prove that for any natural number $n$, $n<$ the cardinality of continuum. Prove that Cardinality of the power sets of the naturals < the cardinality of the power set if the reals. Prove that there is no largest cardinal number. Prove that if there…
user147051
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Proving a contrapositive statement for Mersenne primes

Prove that: If n is not prime, $2^{n}-1$ is not prime. I tried to make a sub, but that's unfeasible, so not sure what to do now.
Enshu Liu Dongfang
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How can I appropriately prove something in a proof(in other words, make a subproof) and refer back to it later in the proof

I am relatively new to number theory, and wanted to ask how to appropriately write a “subproof” within a proof. I searched the internet for a solution and came across “lemmas” but am not sure if I can create my own lemma within a proof and refer to…
Shaurya Jeevagan
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Prove that there exists a polynomial $p(x)$ such that $|p(\theta)-\cos \theta|$ less than or equal to $10^{-6}$

I managed to prove until $|\cos x|$ less than or equal to $1$, but not sure how to continue, please help
omelette
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Confusion about contrapositive of "if $n$ is even then $2n$ is even"

The given statement is "If n is an even integer, then 2n is also an even integer". First we tried to prove it with the direct proof. let's assume that n is an even integer that, n = 2K, where K belongs to integers Therefore, by substituting n = 2K…
Woshi
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Prove there exsits some $k\in \Bbb R$ such that $k^4+4t^2+5\lt0$.

Deduce whether the statement is true or false. N: If (for any $s,t \in \Bbb R, s^5-st+t^2\geq0$) then (there exsits some $k\in \Bbb R$ such that $k^4+4t^2+5\lt0$). I'd like to ask isn't it always true that $k^4,t^2$ must be positive for any real…
sunny
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How do I procced from here for this proof?

Show that if $f_n^2$ converges to $l^2$ then $|f_n|$ tends to $|l|$ as n tends to infinity. My attempt: Since $f_n^2$ converges to $l^2$, it is bounded. Let $k$ and $K$ be its lower and upper bound respectively. This implies, $k\leq f_n^2\leq…
Natasha J
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Why is the difference between two odd squares multiples of $3$ is divisible by $72$?

Why is the difference between two odd squares multiples of $3$ is divisible by $72$? Here is my solution and I am not sure what should be next. Note that any odd number is in the form of $2m+1$ Here we take $m$, $n$ so that …
PRD
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Sequence Induction Proof

Q: Let $(x_n)$ be a real sequence satisfying that every subsequence of $(x_n)$ does not converge in $\Bbb{R}$. Prove that $\vert{x_n}\vert$ $\implies$ $\infty$ as $n$ $\implies$ $\infty$. My lecturer left this as an exercise that he didn't give the…
Sam Connell
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2 answers

Prove or disprove: There exist real numbers $x$ and $y$ so that $x - y$ is rational and $x + y$ is irrational.

I believe the statement is false. Because in order for $x + y$ to be rational, both x and y must be rational, and in order for $x + y$ to be irrational, either $x$ or $y$ must be irrational. I'm just not sure how to prove it. I'm trying to prove the…
user831363
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