For questions about the writing of proofs. But instead of focusing the mathematics behind the proof, these questions ask about the details and implementation of the proof.

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0
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1answer
60 views

Epsilon delta proof

I know that the point of the proof is to show that you can get within $\epsilon$ of the limit, by giving a value that is within $\delta$ of $x$. But when solving for $\delta$ in terms of $\epsilon$ ...
-3
votes
1answer
33 views

Proof of Theorem of Divergent Sequences [closed]

Let's say $(a_n)$ and $(b_n)$ are divergent sequences. Show or disprove the following: $((a_n b_n)_n)$ is divergent. $((a_n + b_n)_n)$ is divergent. $((c b_n)_n)$ with $c\neq0$ is divergent. ...
0
votes
0answers
40 views

Mathematical logic and proofs involving absolute values

Is the following proof correct? Let ($\forall$ x, y $\in $$\Bbb R)$ $|x-y| \le |x| +|y|$ case#1: Suppose x and y $\ge0$. We want to show that $|x-y| \le |x| + |y|$. Since $|x|\ge x$ and $|y|\ge y$, ...
0
votes
1answer
33 views

Are these proofs correct?

I haven't formally learn how to do proofs, but I attempted some of these. It'd be great if you guys can check them and give me some pointers. Thanks!
3
votes
3answers
81 views

If a connected graph has a unique spanning tree, then it is a tree.

Prove if a connected graph has a unique spanning tree, then it is a tree. Edit: This can be shown with proof by contradiction.
2
votes
1answer
36 views

Is this proof by induction correct?

Prove by induction that for all $n\in\mathbb N$, $3\mid n^3+3n^2+2n$. $$P(1) = (1)^3+3(1)^2+2(1) = 6$$ Which is clearly divisble by $3$. Therefore, $P(1)$ is true. Assume $P(1),\ldots,P(n)$ and ...
0
votes
1answer
29 views

Let $G$ be a graph with radius $r$ and let $x$ be a vertex in the center of $G$. If $d$($x,y$)=$r$, then $y$ is in the periphery of $G$

Prove, disprove, or give a counterexample: Let $G$ be a graph with radius $r$ and let $x$ be a vertex in the center of $G$. If $d$($x,y$)=$r$, then $y$ is in the periphery of $G$. Eccentricity - the ...
0
votes
1answer
33 views

If a tree has order 2 or more, then the minimum cut set is 1. [closed]

Prove: If a tree has order 2 or more, then the minimum cut set is 1.
0
votes
1answer
25 views

Suppose $f:X\to Y$ is onto and $A\subseteq Y$. Then $f(f^{-1}(A))=A$.

Prove, disprove, or give a counterexample: Suppose $f:X\to Y$ is onto and $A\subseteq Y$. Then $f(f^{-1}(A))=A$. Edit: Does this work? Suppose $f:X \to Y$ is onto and $A \subseteq Y$. We know ...
1
vote
0answers
21 views

Second Derivative of Holomorphic function According to Cauchy's

I am asked to prove that, supposing f is holomorphic on the region G, w $\in$ G and $\gamma$ is a positively oriented, simple, closed, smooth, G-contractiblecurve such that w is inside $\gamma$ , we ...
1
vote
1answer
44 views

Is this equation for $2^k!$ correct?

I couldn't find any equation for $2^k!$ so I came up with an equation that appears to work for the factorial of a power of $2$. However, I'm having problems proving it. My equation: $$ \def\x{\times} ...
0
votes
1answer
29 views

Proof that any self-complementary graph has to have $4k$ or $4k+1$ vertex, for some $k \in \mathbb N$

I've seen looking on previous questions that using this algorithm, I can construct self-complementary graphs. I got confused at this point, because I'm not sure if I should proof that there are no ...
2
votes
1answer
23 views

Proof-Writing $\theta(n) \le \theta(2^{k+1}) < 4*log[2n]$

At the end of this message there are two steps that I do not understand. The proof wants to show in the end that : *$\theta(n) \le \theta(2^{k+1}) < 4*log[2n]$ by definition we have ...
0
votes
1answer
18 views

Help proving a theorem in my textbook

If $r \in \mathbb{N}$ is not a perfect square, then $\sqrt{r}$ is irrational. For reference, an integer $n$ is a perfect square if $n=m^2$ for some $m \in \mathbb{Z}$. Any help proving this ...
2
votes
2answers
45 views

Help with a proof my professor gave my class

Let $x,y \in \mathbb{R}$ with $x<y$. There exists an irrational number $z$ such that $x<z<y$. My proof so far: Let $x,y \in \mathbb{R}$ and assume $x<y$. Then, by Theorem 11.8 (in ...
0
votes
1answer
20 views

Equivalence relations proof

I need to prove that if $R_1$ and $R_2$ are equivalence relations on the set $A$, then $R_1\cap R_2$ is an equivalence relation. Problem is I dont know how. Please help!
0
votes
1answer
33 views

Combinatorics Proof

I am having trouble with a combinatorics proof. I need to prove that if $r$ <= $n$ then the number of $r$ - subsets of {1,...,n} is $n!$/$(n-r)!$*$r!$ I really struggle with writing proofs and ...
0
votes
1answer
27 views

Discrete Math Proofs, Partial Orders and Equivalence Relations

I am horribly stuck on $3$ proofs for my discrete math class. Any help would be greatly appreciated. Prove that if $R$ is a partial order, then $R^{-1}$ is a partial order Prove that if $R_1$ and ...
1
vote
2answers
39 views

Finding quantity of vertex of odd degree in a graph

Let $G=(V,X)$. If $G$ has n vertex, such exactly $n-1$ have odd degree, how many vertex of odd degree have $\overline {G}$. ($\overline {G}$ the complement of $G$.) So the first thing I notice is ...
2
votes
1answer
16 views

Proof that in a graph of $2$ or more vertrex, there's at least $2$ of them that have the same degree

That's what I what to prove let $G$ be an undirected graph such it has $2$ or more vertex, there's at least $2$ vertex that have the same degree. I'm almost certain that, supposing that it's possible ...
2
votes
0answers
111 views

Can you share your experience in hand waving and other informal communication regarding mathematical proofs?

I intend to write a paper that will address among other issues the informal communication between mathematicians. My point of origin is the view that every proof can be represented by a sequence of ...
3
votes
2answers
49 views

Proving limit of a sum

I need to prove the following: $$\lim_{s \to \infty} \sum_{n = 1}^\infty \frac 1 {n^s} = 1$$ This is my attempt: \begin{align} \lim_{s \to \infty} \sum_{n = 1}^\infty \frac 1 {n^s} & = \lim_{s ...
0
votes
1answer
28 views

Error replacing integral of f with its midpoint rule approximation

here is a question I've been banging my head against. If f is continuous on [a,b] and differentiable on (a,b), and if there is a positive real number M such that |f'(t)| is less than or equal to M ...
1
vote
2answers
44 views

What is the proper way to prove this?

First of all, here is the question I am trying to answer for context. I can see that the statement $\forall x \in \mathbb{Z} , \exists y \in \mathbb{Z}((x\leq y ) \wedge (x+y=0)) $ negates to ...
0
votes
3answers
58 views

Help with 2 questions my professor gave us

I was wondering how to solve these two proofs my professor put on the blackboard today. He said they were pretty easy but i'm still unsure how to prove them. ANy help would be greatly appreciated! ...
-1
votes
2answers
33 views

Show with an exemple that the inclusion could be real

Im trying to Solve this problem. I have started to Solve the first part, but need to show it with an example. Thankfull for help.
0
votes
1answer
20 views

Unsure how to solve this proof

I came across this in my textbook and was wondering how it could be proved. My only thought is that contradiction should be used. Thank you for any help! Suppose $L = \lim_{k \to \infty} X_k$. ...
3
votes
2answers
38 views

Disjoint Cycles and Supports

I am working though an Introduction to the theory of Groups. I have come the following exercise: "Let $\alpha = \begin{pmatrix} i_1 & i_2 & \cdots & i_r \end{pmatrix}$ and $\beta = ...
1
vote
1answer
38 views

Permutation cycles

My tasks are the following : Task 1 : Prove that $ \begin{pmatrix} 1 & 2 & \cdots & r-1 & r \end{pmatrix} = \begin{pmatrix} 2 & 3& \cdots & r & 1 \end{pmatrix} ...
0
votes
1answer
54 views

Proofing a Reachable Node Algorithm for Graphs

I am trying to proof the following algorithm to see if a there exists a path from u to v in a graph G = (V,E). ...
2
votes
2answers
57 views

How to complete this epsilon delta proof

Prove $\lim_{x\to 1} {2+4x \over 3} = 2$ using the epsilon delta definition of a limit. if $0 < \left|x-1\right| < \delta$ then $\left|{2+4x \over 3}-2\right| < \epsilon$ scratch work for ...
2
votes
0answers
75 views

Proof of uniform continuity on compact sets

Show that a function $f:\mathbb{R} \rightarrow \mathbb{R}$ that is continuous on a compact set $K$ is uniformly continuous on $K$. Is the proof below correct? Proof: Let $\epsilon > 0$ and let ...
1
vote
1answer
32 views

Constant function with maximum modulus [duplicate]

Suppose that $f$ is analytic on a domain $D$, which contains a simple closed curve $\gamma$ and the inside of $\gamma$. If $|f|$ is constant on $\gamma$, then I want to prove that either $f$ is ...
-1
votes
3answers
50 views

Show that $C(n,k) = C(n-1,k) + C(n-1,k-1)$ [duplicate]

I'm studying for my final for Statistics, and I want to understand literally every problem in my textbook (at least in the first 7 chapters). One of the problems asks to show that ${n}\choose {k}$ ...
1
vote
1answer
67 views

Minimum Modulus Principle for a constant fuction in a simple closed curve

Suppose that $f$ is analytic on a domain $D$, which contains a simple closed curve $\gamma$ and the inside of $\gamma$. If $|f|$ is constant on $\gamma$, then I want to prove that either $f$ is ...
0
votes
2answers
38 views

Usage of Maximum Modulus Theorem?

I have a function $f(z)=ze^z$, I want to find the maximum value of $|f(z)|$ as $z$ varies over the region $D=\{x+iy: x^2+y^2\leq 4, x,y\geq 0\}$. I was thinking that this is case where I can use the ...
1
vote
2answers
60 views

Let $G$ be a connected graph. If $G$ has no cut vertices, then G has no bridges.

Prove, disprove, or give a counterexample: Let $G$ be a connected graph. If $G$ has no cut vertices, then $G$ has no bridges.
1
vote
1answer
27 views

If the edge $xy$ is a bridge of $G$, then $x$ and $y$ are in separate components of $G$-$xy$.

If the edge $xy$ is a bridge of $G$, then $x$ and $y$ are in separate components of $G$-$xy$. I can't think of a counterexample so I am operating under the impression that it can be proved. How does ...
1
vote
1answer
61 views

Proof using addition and multiplication axioms

I'm working on addition and multiplication axioms of integers for discrete math. I'm trying to prove (k - m) + (m - n) = k - n. The first step I took was this ...
2
votes
2answers
53 views

Logic Proof with Natural Deduction: if I assume the antecedent, do I still have to prove the consequent?

I have the unpleasent feeling that my "proof" is dead wrong. The core of my concerns is: when I have something like A -> (B -> C) and I assumed ...
1
vote
3answers
62 views

Prove that a graph with $n$ vertices and less than $n$-1 edges, is disconnected.

Prove that if $G$ is a graph with $n$ vertices and fewer than $n$-1 edges, then $G$ is disconnected. The book I am working through uses a similar definition of "$n$ vertices and at least $n$-1 edges, ...
0
votes
2answers
45 views

Prove the following Statement is a tautology

I need to prove the following statement is a tautology [¬Q∧(P→Q)]→¬P So far this is what i have but now i am stuck any advice on further finishing this problem would be helpful. ...
0
votes
4answers
64 views

Integral Problem $\sin^6 x$. [closed]

What is the integral of $\sin^6 x$? Can some one publish it with the method it would be really helpful. Specially I want the trig identities.
0
votes
1answer
22 views

Proving a circuit of a graph will have an edge in common with a cycle of the same graph.

Prove, if possible, if an edge lies on a circuit in $G$, then the edge also lies on a cycle in $G$. I attempted to find a counterexample but it seems pretty evident that this statement is true. The ...
0
votes
1answer
25 views

Need help with compositions of relations

Prove that given relations $R_1 \subseteq A \times B$, $R_2 \subseteq B \times C$, $R_3 \subseteq C \times D$ then $(R1 \circ R2) \circ R3 = R1 \circ (R2 \circ R3)$ I don't know where exactly to ...
1
vote
1answer
18 views

inductive proof of binary existence

Can someone help me witha well exlpained inductive proof of option 2 problem 2. I ha e read many different ones but they dont really make sense to me and I need to know how to do this for my final. ...
1
vote
1answer
31 views

First derivative test and uniqueness of local extrema

This is the context in which my question lies. See below for the actual question. Let $f(x)$ be differentiable everywhere and have a minimum at $x^*$. Then for every $x$ in a proper neighbourhood ...
0
votes
3answers
33 views

Help solving a proof

My professor put this up on the blackboard and I was wondering how to solve it. Let $x,y \in \mathbb{R}$. Then |$x$|< |$y$| if and only if $x^2 < y^2$.
2
votes
0answers
101 views

Finding minimum graph of $k$ disjoints component

Sorry for the english, I tried to make it the most clear possible. Be $G$ a connected graph not directed, I have to find an algorithm that given $n$ the quantity of vertex and $0<k<n$ disjoint ...
1
vote
1answer
27 views

Let $A =[a,b,c,f,g,i], B=[b,f,h]$ and $ C = [a,k,l,m]$ Show that $\backslash$ is not associative

Question : Let $A =[a,b,c,f,g,i], B=[b,f,h]$ and $ C = [a,k,l,m]$ Show that $\backslash$ is not associative by comparing $(A \backslash B) \backslash C$ with the set $A \backslash(B \backslash C)$. ...