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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I need to know how to represent the addition and multiplication of two elements in this set

The question is Consider $\mathbb Z \left[\frac{1}{10}\right] = \{\frac{a}{10} \mid a\in\mathbb Z\}$ under addition and multiplication. Is it a ring? Is it commutative? is the set really just all the elements: $$\frac{1}{10}=\frac{1}{10},\space…
K. Gibson
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Strong vs weak induction

My professor in a proof class said very explicitly several times that "strong induction is a more powerful proof technique then weak induction and is preferred over weak induction". Anywhere I have looked online and in textbooks it says that weak…
Mark
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Question on 'without loss of generality'

Suppose I want to prove that a sequence $(s_n)$ converges, and I don't know much more about $(s_n)$ than a few properties. (That is, I don't know a closed-form formula.) I have seen a proof written by my professor that began with "we're concerned…
user465188
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How do you learn to write proofs? & how to prove that if $f: A \to B$ is a surjection, then $f$ has a right inverse?

Hello fellow math enthusiasts, I am currently in a proof based class but am struggling to even understand how to write a proof. Whenever the teacher or fellow classmates write proofs none of the things they write or say make sense. This entire…
DeeJP
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Is this a norm on $L^{p}([0,1])$?

Let $0< p< 1$ and let $\|f\| _{p}$ be defined as $(\int_{0}^{1} |f|^p)^{1/p}.$ Prove or disprove: $\|\cdot\|_{p}$ is a norm on $L^{p}([0,1])$ My trial: It is a norm, but I am unable to prove the triangle inequality? Could anyone help me in this?
Emptymind
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Can we place two exact cubes between two exact neighbor squares?

In other words are there any integers that satisfy the following inequality: n² < a³ < b³ < (n +1)²? I have no idea how to solve the problem? Can someone give me a hint? I know this question is related to proof by contradiction.
Jerry Lyu
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Proof optimization in mathematics

In computer science there is a concept of string complexity, called kolmogorov complexity, which basically says that the complexity of a string is the length of the smallest program that prints that string. If we take the formal proofs of…
Yamar69
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Proof Help: Membership Table

I am new to proofs with membership tables and this is the last question I am posting. I am trying to teach myself discrete math and am stuck on this: Let $ A, B$ and $C$ be sets in the universal set U. By making a membership table, prove that…
JustaBreitGuy
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$1^3+2^3+...+n^3= $? How I can find formula

$1^3+2^3+...+n^3=$ has a formula which $(1+2+3+...+n)^2 $ or $[n(n + 1)/2]^2$ . We can verify with ınduction and I know how I can prove it. How we find what is the formula... I tried like this $1^3+2^3+...+n^3= An^4+ Bn^3+Cn^2+Dn+E$ after a long…
David
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New to proofs, need help with how to approach a beads-and-wires proof puzzle

I am working on a proof puzzle about beads and wires. We are given 4 axioms about the objects you can create with beads and wires. Axiom 1. You must have exactly 3 beads. Axiom 2. There is exactly one wire between each pair of beads. Axiom 3. Not…
qmild
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Negation of "...then $n$ has at least one prime factor $p$ with $1 \lt p \le \sqrt{n}$" for a proof by contradiction.

This is what I'm trying to proof: If $n$ is a positive composite number, then $n$ has at least one prime factor $p$ with $1 \lt p \le \sqrt{n}$ But I'm a bit confused about how to properly negate the conclusion so I can use contradiction. First, I…
Dr. Pulque
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Guidelines on using Proof by Contrapositive

I am fairly new to writing proofs and am having difficulty understanding when to use a proof by contrapositive. A truth table clearly shows that $\neg Q\implies\neg P$ implies that $P\implies Q$. Given true propositions to prove, this is not much…
Lisa K
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Proving Euler's product formula for sine

Is the following a proof of Euler's product formula for sine (see (8) below)? If no, then why? The sine can be a polynomial by the taylor series for sine, which coverage for all $x \in \mathbb{R}.$ As known, the roots of this polynomial are…
Ziv Sdeor
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Prove that for all real numbers x and y there is a real number $z$ such that $x + z = y - z$

This one must be pretty basic, but... Prove that for all real numbers $x$ and $y$ there is a real number $z$ such that $x + z = y - z$ I am quite confused about how you need to prove this. My attempt was: $$\tag1 x + z = y - z$$ $$\tag2 2z = y…
Stokolos Ilya
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Does RMS of a sequence of values equate to the RMS of the Fourier Transform of the same sequence of values?

Firstly - I am not working in the maths field, (so please be gentle), but I find maths interesting and would like to learn more while the brain-cells still permit. I was posed a question recently which I need assistance with. It relates to the…
Mark
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