For questions about the formulation of a proof, not about the mathematics behind it.

learn more… | top users | synonyms

0
votes
0answers
10 views

Find the volume of h(P) in terms of volume of P

Where h:$\mathbb R^n \rightarrow R^n$ is the function h(x) = $\lambda x$ and P is a k-dimensional parallelopiped in $\mathbb R^n$ Attempt at the solution : Let $x_1,....,x_k$ be vectors in $R^n$ ...
1
vote
1answer
42 views

Is it necessary to prove equality from both sides?

I have asked this question yesterday, and my friend told me, to rememeber to "prove it" also from the other side e.g. Let x $\in$ Conv($M+u$).....then $x$ $\in$ Conv($M$)+ $u$. Why would somebody ...
1
vote
0answers
37 views

Help on Big O proof

I need some help with a big O proof. I think I have a proof but I feel like some of the steps aren't logically compatible. The Question: For all functions f,g with domain $\mathbb{N}$ that maps to ...
4
votes
2answers
122 views

What exactly is the 'induction trap'

I've looked everywhere, and I've looked at a lot of examples. I don't quite understand what about the induction trap is so wrong. The most common example is the graph theory tree example (page 5 here: ...
2
votes
1answer
74 views

Let $1 + 2^m = 3^n$. What the max value of $(m+n)$?

How do I determine the maximum value of $(m+n)$ if $m$ and $n$ are natural numbers if $1 + 2^m = 3^n$ holds? I have got $\text {max} (m+n)$ to be $5$ so far, but I do not know how to determine whether ...
1
vote
0answers
32 views

How to generate/validate unique fractal?

There are many known fractals that exist such as Mandelbrot, Cantor set, or the Koch curve, Sierpinski Triangle. What I am curious about, is how one could go about creating their own, unique fractal ...
0
votes
0answers
41 views

Let $A,B,C$ be sets such that $\mathcal{P}(A) \cup \mathcal{P}(B) = \mathcal{P}(C)$. Then either $A=C$ or $B=C$.

Let $A,B,C$ be sets such that $\mathcal{P}(A) \cup \mathcal{P}(B) = \mathcal{P}(C)$. Then either $A=C$ or $B=C$. I just need a little direction with this. I know that since $\mathcal{P}(A) \cup ...
1
vote
1answer
26 views

Let $A,B \subseteq X$. If $A \subseteq B$, then $(X\setminus B) \subseteq (X\setminus A)$

Let $A,B \subseteq X$. If $A \subseteq B$, then $(X\setminus B) \subseteq (X\setminus A)$. Using a sort of diagram I can easily convince myself this is true. I assume I must use a proof by ...
2
votes
1answer
40 views

Proof by contradiction to this inequality

Prove, by contradiction, that if $w$, $z$ $\epsilon$ $\mathbb{C}$ such that $|w|$ $\leq 1$ and $$w^{n} z + w^{n - 1} z^2 + \cdots+ wz^n = 1$$ then $|z|$ $\gt$ $\frac{1}{2}$ I have been thinking ...
2
votes
2answers
34 views

True or false: the contrapositive statement of “$\text{not } A\implies \text{not } B$” is “$A\implies B$”?

Question : State whether 'True' or 'False' and justify your answer giving reason. The contrapositive statement of "$\text{not } A\implies \text{not } B$" is "$A\implies B$" where $A$ and $B$ ...
1
vote
2answers
32 views

Show that rational cosets are either identical or disjoint

Let $\mathbb{Q}$ denote the set of rational numbers. Let $x,y \in \mathbb{R}$. Let $A_x = x+ \mathbb{Q} , A_y = y+ \mathbb{Q} $ Can someone help me in simple arguments prove that cosets $A_x, A_y$ ...
0
votes
2answers
43 views

Question about 'strong' assumptions and proving 'strong' result.

When someone says "we can prove a stronger result", it means the new statement is more general and better than the previous. However, when we add conditions to an argument, add more assumptions, we ...
0
votes
1answer
53 views

Why does $\lim_{x \to \infty} \frac{n^x + x^2}{n^x +x} = 1$ for a constant $n \gt 1$?

Why does $\lim_{x \to \infty} \frac{n^x + x^2}{n^x +x} = 1$ for a constant $n \gt 1$ but infinity when constant $n \leq 1$ ? I understand intuitively that when $n$ is less than or equal to $1$, $n^x$ ...
0
votes
1answer
37 views

NEUTRAL GEOMETRY PROOF. prove that a figure can have at most one center of symmetry

A center of symmetry for a figure F is a point O such that every line through it cuts F in two points, P and P', such that O is the midpoint of PP'. Prove that a figure can have at most one center of ...
2
votes
1answer
67 views

What is the most basic way to show that $\emptyset \in S$

Let $S$ be a set, what is the most basic way to show that $\emptyset \in S$? I am asking because sometimes a question in involving a topology $\tau$ or a $\sigma$-algebra $\Sigma$ will want you to ...
1
vote
0answers
20 views

Computing $\alpha^*w$ in general

Let $A$ be open in $R^k$, let $\alpha : A \rightarrow R^n$ be of class $C^\infty$. Let $x$ denote the general point of $R^k$, let $y$ denote the general point of $R^n$ If $I = (i_i, ...,i_l)$ is an ...
0
votes
0answers
15 views

Show that $\alpha^*(dy_i) = d(\alpha^*y_i) $

where $y_i:\mathbb R^n \rightarrow R$ is the $i^{th}$ projection function in $\mathbb R^n$ Given: Let A be open in $R^k$; let $\alpha: A \rightarrow R^n$ be a $C^{\infty}$ map. Let x denote the ...
2
votes
1answer
48 views

Proof of a Four-Pole Tower of Hanoi

Four-Pole Tower of Hanoi: Suppose that the Tower of Hanoi problem has four poles in a row instead of three. Disks can be transferred one by one from one pole to any other pole, but at no time may a ...
1
vote
0answers
28 views

If $|ax^2+bx+c|\le1$ for $|x|\le1$(redundant?), then prove that $|cx^2+bx+a|\le2$ for $|x|\le1$. [duplicate]

If $|ax^2+bx+c|\le1$ for $|x|\le1$, then prove that $|cx^2+bx+a|\le2$ for $|x|\le1$. $a,b,c$ are real. I discovered this to be a duplicate of $|px^2+qx+r|\le1$ for all $x$ in $[-1; 1]$, show that ...
0
votes
3answers
49 views

prove the Limit of the sequence $A_{n}$, when $A_{1} = \sqrt{3}$ and $A_{n+1} = \sqrt{3A_{n}}$

is it sufficient to show that since the limit of a sequence $A_{m}$ where $\forall m, \;A_{m}=\sqrt{3}$ is just $\sqrt{3}=3^{\frac{1}{2}}$, the limit of $A_{n}$ will be 3 to some power? I know from ...
0
votes
2answers
55 views

Prove that $7^{\frac 14}$ is not rational using the Unique Factorization Theorem.

I am currently trying to prove this using the Unique Factorization Theorem and I am stuck. I attempt to prove this BWOC and assume $7^{\frac 14}$ is rational so that it can be expressed as $\frac ...
1
vote
1answer
37 views

Show that monotonicity directly follows countable additivity

In these notes http://math.gmu.edu/~dwalnut/teach/Math776/Spring11/776s11lec03_notes.pdf it says countable additivity implies monotonicity of measure I want to show that $\mu(\bigcup_{k = 1}^\infty ...
0
votes
1answer
48 views

How can I prove that the centers of three overlapping squares and the shared point form a parallelogram?

Consider a square. Let $P$ be any point on the base of the square. Connect each of the upper vertices to this point and use these segments as sides to create two more squares (outward). The picture ...
1
vote
1answer
74 views

What words do you use to describe a bad proof?

I was writing up a proof, but wasn't satisfied with what I was coming up with. The logic is there, but I wasn't able to express it clearly in math lingo. I was about to describe my work as "floozy" ...
1
vote
2answers
37 views

Let $G$ be a group and $H_{1},H_{2}\leq G $. Then $H_1 \cup H_2 \leq G \iff H_1 \subset H_2$ or $H_2 \subset H_1$

Let $G$ be a group, $H_{1},H_{1} \leq G $. Then $H_1 \cup H_2 \leq G \iff H_1 \subset H_2$ or $H_2 \subset H_1$ I'm stucked at this very trivial proof of groups. Here's my attempt: $(\Leftarrow)$ ...
0
votes
1answer
24 views

if $d$ is the greatest common divisor of $a, b \in \mathbb{Z}$ show that $(a) + (b) = (d)$

I've got the basic idea of this proof just not sure how to write it formally. If $d = gcd(a, b) $, then $ d = au + bv $, where $a$ and $b$ are not both zero. $(d)$ is the set of all multiplies of ...
1
vote
1answer
35 views

If R is a commutative ring, but has no identity is c and element of I

Problem statement: Let $c \in R$ and let $ I = \{rc\mathrel{|}r\in R\} $ If R is a commutative but has no identity, is c an element of the ideal I. Proof: Suppose $c \notin I$ and R is a ...
0
votes
0answers
22 views

Proving Infinitely Ascending Chain of Subobjects

How would you prove that an infinitely ascending chain of subobjects of an object $X$ in $\mathcal{C}$ is stationary given that only finitely many preorders in the chain that are not isomorphisms in ...
1
vote
3answers
43 views

Show that there are infinitely many positive integers A such that 2A is a square, 3A is a cube and 5A is a fifth power.

Show that there are infinitely many positive integers A such that 2A is a square, 3A is a cube and 5A is a fifth power. Using some arithmetic, I felt that if $A = 2^{15k}3^{20k}5^{24k}$ then it ...
4
votes
1answer
46 views

Show $\dbinom{a}{b}\dbinom{b}{c}=\dbinom{a}{a-c}\dbinom{a-c}{a-b}$

I am trying to give a non-algebraic proof for this equality: $$\dbinom{a}{b}\dbinom{b}{c}=\dbinom{a}{a-c}\dbinom{a-c}{a-b}$$ So far, I could only use the identity $\dbinom{x}{y}=\dbinom{x}{x-y}$. ...
0
votes
0answers
22 views

Writing a linear transformation in terms of elementary alternating k-tensors

Let T: $\mathbb R^m \rightarrow R^n $ be the linear transformation T(x) = Bx If $\alpha_I$ is an elementary alternating k-tensor on $\mathbb R^n$, the $T^*\alpha_I$ has the form $T^*\alpha_I = ...
3
votes
3answers
736 views

Proof involving twin primes

I have to prove that if $p$ and $p+2$ are twin primes, $p>3$, then $6\ |\ (p+1)$. I figure that any prime number greater than 3 is odd, and therefore $p+1$ is definitely even, therefore $2\ |\ ...
-1
votes
2answers
184 views

How to study for hard math proofs?

Most of the content is new to me and there are a lot of theorems and proofs that I am learning; not that I need to know all of them but I enjoy to learn more. Some of the concepts (like open sets) or ...
0
votes
0answers
13 views

Why FFT algorithm (Cooley-Tukey) takes O(nlogn)?

I was wondering how this algorithm can be formally interpreted with an upper bound n*log(n). There's some formal proof for this? I would appreciate if somebody can help me. Thank you.
0
votes
0answers
12 views

Verify $T^*(f^\sigma)$ = $(T^*f)^\sigma$

Where $T^*$ is linear. $f^\sigma(v_1,...,v_k)$ = $f(v_{\sigma(1)},...,v_{\sigma(k)}) $T^*f(v_1,...,v_k)$ = $f(T(v_1),...,T(v_k))$ Attempt at the proof: I didn't use the fact that T is linear ...
1
vote
2answers
43 views

Help with set bijection proof

Let $f: M \to N$ be a bijection Let $A, B \subset M$ Then show: $f(A \cap B) = f(A)\cap f(B)$ $f(A^c) = f(A)^c$ I have no idea how to do this honestly! How do you go about doing this? Can you ...
0
votes
4answers
31 views

Show that $\sum_{i=1}^n a_i p_i=1$ if and only if $p_i=1$ when $0<a_i<1$, $\sum_{i=1}^n a_i=1$, $0\leq p_i\leq 1$

Consider $n$ real numbers $0<a_i<1$ such that $\sum_{i=1}^n a_i=1$ Consider other $n$ real numbers $0\leq p_i\leq1$. Could you help me to show that $\sum_{i=1}^n a_i p_i=1$ if and only if ...
1
vote
1answer
34 views

Proof by contradiction using divisibility

Prove by contradiction that if b is an integer such that b does not divide k for every natural number k, then b=0. I understand to begin by assuming the false statement: There exists an integer b ...
1
vote
2answers
44 views

Logarithm proof by contradiction [closed]

Prove by contradiction that $\log_5 8$ is irrational. While I understand that this is true, I am struggling to prove it by contradiction. Thank you for any help!
1
vote
2answers
24 views

Proving set statements

Let A = {x ∈ Z: x = 5a + x for some integer a} B = {y ∈ Z: y = 10b - 3 for some integer b} C = {z ∈ Z: z = 10c + 7 for some integer c} Prove or disprove the ...
0
votes
1answer
13 views

FToA: $P(z)$ can be factorized into linear terms $\in \mathbb C$ (it's roots). Then $P(z)$ can be factorised into REAL linear and quadratic terms.

By the FTA I know that every non-constant polynomial has at least one root. Then I can show that it can be factorized into $deg(P(z))$ linear terms. Now I'm trying to show the corollary: It ...
0
votes
1answer
12 views

proving a value is less than or equal to another value

how would i prove that $\frac{1}{n!}\le \frac{1}{2^{n-1}}$ for $n \ge 1$ i checked $P(1)$ and it is true. and now I'm on $P(n+1)$ and plugged it in $\frac{1}{(n+1)!}\le ...
1
vote
2answers
56 views

Prove that if $H \le G$, then the identity in $H$ is the same as the identity is $G$

My question is a generalization of a result I saw in Linear Algebra. Prove that if $H \le G$, then the identity in $H$ is the same as the identity in $G$. I would like to know if my ...
0
votes
1answer
26 views

How to prove that the following predicate formula is valid…

I've been having trouble with proving validity in predicate logic. A question was given to us during a lecture that I was not able to attend and so I can't figure out the answer to the following Show ...
0
votes
1answer
27 views

Show that $T^*f$ is an alternating tensor if f is an alternating tensor

Show that if T: V $\rightarrow $ W is a linear transformation and if f $\in A^k(W) $ then $T^*f \in A^k(V)$ where $T^*$ is the dual transformation. Attept at the solution: If $f \in A^k(V)$ and ...
0
votes
0answers
26 views

Experimenting With Algebraic Abstraction

I am a novice attempting to understand the "abstract" components of mathematics. Consequently, I have devised mathematical statements that I would like to be verified by knowledgeable users using the ...
2
votes
1answer
35 views

How to prove: $\bigcap_{n=1}^{k}(n, \infty) \neq \emptyset$?

How to prove that for every natural number $k >= 1$, the following holds: $\bigcap_{n=1}^{k}(n, \infty) \neq \emptyset$ ? I know that for every $k$, all the intervals will have the intersection: ...
1
vote
3answers
51 views

Requesting Clarification Regarding A Proof Drafted By A Novice [closed]

fellow StackExchange users. I am a mathematics novice with a learning disorder requesting verification of a proof that I have devised. The majority of my "mathematical writing" has consisted entirely ...
1
vote
1answer
80 views

Proof using strong induction a conjecture about $4^n$

Compute $4^1$, $4^2$, $4^3$, $4^4$, $4^5$, $4^6$, $4^7$, and $4^8$. Make a conjecture about the units digit of $4^n$ where $n$ is a positive integer. Use strong mathematical induction to prove your ...
0
votes
1answer
41 views

Mathematical induction for particular formula.

I'm currently learning mathematical induction, but I'm not sure how to start a proof for this formula(the problem is different than what I've been practicing with). I'm not looking for the whole ...