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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Eulerian circuit with no isolated vertex is connected

This is my first question (ever), and I am pretty new to math. So I ask for patience and understanding in advance. So this is the proof I came up with: Consider $G = (V,E). $ By definition of Eulerian circuit, $$ \exists\ W: v_0, v_1,\cdots,…
Henri L
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How to derive an proof for this infinite square root equation?

Here is continuous square root, namely: $\sqrt {1 + a \sqrt {1+b \sqrt {1+c\sqrt {1 +...}}}}$= any integer Find $a,b,c,d,e,f,...$ in general Uh, very interesting algebra pre-calculus problem, yet very challenging. I know part of the answer but…
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Proof by induction failure if assumption is wrong?

I never got a clear answer to this question in college. What happens in an induction proof if the assumption is wrong? For example, suppose we try to prove that $n^5$ > n! for n >= $2$ so we start out by stating that when n = $2$ it is true and in…
David
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Show that if A is diagonalizable, then sin^2(A) + cos^2(A) = I. Does this identity also hold for nondiagonalizable matrices?

Show that if A is diagonalizable, then $\sin^2(A)+\cos^2(A)=I$. Does this identity also hold for nondiagonalizable matrices? This is what I got so far: $$ e^{iA}= \cos A +i\sin A \\ \cos A= \frac{e^{iA}+e^{-iA}}{2} \\ \sin A=…
shimura
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If $H,K$ are subgroups of $G$, and $G$ is finite, prove that $[K\colon (H\cap K)]\leq [G\colon H]$

Let $H,K$ be subgroups of a finite group $G$. Prove that $[K\colon (H\cap K)]\leq [G\colon H]$. This is what I have: $[K\colon (H\cap K)] = |\left\{ a(H\cap K) \mid a\in K\right\}|$ $[G\colon H] = |\left\{ bH \mid b\in G\right\}|$ Going this…
Alyosha
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Prove that a function is both differentiable and continous at a point $x_0$

Suppose $f$ is differentialble on $(a,b)$, except possibly at $x_0 \in (a,b)$ an is continous on $[a,b]$; assume $ \lim\limits_{x\rightarrow x_0}f´(x)$ exists. Prove that $f$ is differentiable at $x_0$ and $f´$ is continous at $x_0$. My attempt: If…
user162343
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How to deduce the following trig relation?

How can I deduce: $$\sqrt{|x|}\sin(\frac{1}{x}) \le \sqrt{|x|}$$?? I know of the relation. $$\sin(u) \le u$$ $$u = \frac{1}{x}$$ $$\sin(1/x) \le \frac{1}{x}$$ But nothing related to $\sqrt{x}$ Thanks!
Amad27
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Linear Maps: Prove if $T^2 =0$, then $I-T$ is bijective

Let $V$ be a vector space, $T$ is in $L(V)$, Prove: If $T^2 = 0$, then $I - T$ is bijective. the book also gave a hint: in polynomial algebra, $(1-t)(1+t)=(1-t^2)$ I'm not quite sure where to start. Any help is greatly appreciated!
Sol Morales
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How to prove which of two numbers written as powers is bigger?

Prove which number is larger: a) $10^{100!}$ or $10^{10^{100}}$ b) $e^\pi$ or $\pi^e$ I know we all know how to plug these into the calculator and check, but how someone mathematically prove which one is bigger with words and calculations?
Overclock
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Help explain existence of a limit point of a sequence implies infinitely many $m$ where $d(x,x_m)<\epsilon$

I don't understand the phrase "...all but finitely many elements...". What does this mean exactly and how does the conclusion "Infinitely many elementsof the sequence $\{x_k\}$ must also be within $\epsilon$ of $x$"? I do understand that since the…
mauna
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How do I make this simple proof better (and more correct?)

Let $x$ and $y$ be real numbers. If $x\cdot{y}>\frac{1}{2}$, then $x^2+y^2>1$. Proof: We will prove with the direct method. Let $x$ and $y$ be real numbers. Since $$ x\cdot{y}>\frac{1}{2} $$ it follows that $$ 2xy>1,$$ which means $$x^2+y^2 \geq…
bjd2385
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Show that | and $\downarrow$ are the only binary connectives \$ such that {$} is functionally complete.

I've been reading and coping with van Dalen's Logic and Structure for a a few days. However, I've getting problems to solve his Exercise 6 from Ch 1 Sec 1.3 (p.28). In this exercise, van Daken asks you to show that NAND and NOR are the only binary…
Bruno Bentzen
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Uniform convergence on an interval

Let $a
Diya
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Theorem 1.20 (b) in Baby Rudin: Can the proof of the theorem be improved?

I'm reading Principles of Mathematical Analysis, third edition, and am at Theorem 1.20(b), which is as follows: If $x \in \mathbb{R}$, $y \in \mathbb{R}$, and $x < y$, then there exists a $p \in \mathbb{Q}$ such that $x< p < y$. Now here is the…
Saaqib Mahmood
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In proof by induction, what happens if P(n) is false for a specific case or the base cases are false? Can we still deduce meaningful conclusions?

The principle of mathematical induction works basically because of the following: If we have a predicate $P(n)$, then if we have: P(0) is true, and P(n) $\implies$ P(n+1) for all nonnegative integers n, then: P(m) is true for all nonnegative…
Charlie Parker
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