# Tagged Questions

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

2answers
647 views

### Using the Pumping Lemma to Prove $L = \{a^ib^jc^k \mid i < j < k\}$ is not Context-Free

I want to use the Pumping Lemma to prove that $$L = \{a^ib^jc^k \mid i < j < k\}$$ is not context-free. I think I have the intuition, but I don't know how to prove it. Help?
1answer
42 views

### The image of an injective function whose domain is a topological space also a topology

Let $(X, T )$ be a topological space, and let $f : X → Y$ be an injective (but not necessarily surjective) function. QUESTIONS. (1) Is $T_f := \{ f(U) : U ∈ T \}$ necessarily a topology on $Y$ ? ...
3answers
92 views

### Using $\epsilon-\delta$ proof to prove continuity

Use an $\epsilon-\delta$ proof to show that $f : R \setminus \left \{ \frac{-3}{2} \right \} \rightarrow R$ , $$f(x) = \frac{3x^2-2x-5}{2x+3}$$ is continuous at $x = -1$ Hello there. Can anyone ...
1answer
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### Proof using mean value theorem

Prove using the mean value theorem that $e^{x+1}\geq 2e^x$ by considering the interval $[x,x+1]$. Using the definition, there exists a $c$ in $(x,x+1)$ such that $e^{x+1} - e^x = e^c$ (this is of ...
1answer
59 views

### how to prove $G$ is an abelian group under $*$ (called the real numbers mod 1)

Let $G = \{x \in \mathbb{R}~|~0\leq x < 1\}$ and for $x,y \in G$ let $x*y$ be the fractional part of $x+y$ i.e $x*y = x + y - [x + y]$ where $[a]$ is the greatest integer less than or equal to $a$. ...
4answers
2k views

1answer
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### Show that an event has strictly positive probability

Consider the random variables $W_i,W_j, X_i, X_j$ with $X_i\sim X_j$, $X_i\perp X_j$ and $W_i\sim W_j, W_i\perp W_j$, where $\sim$ denotes equal probability distribution and $\perp$ denotes ...
3answers
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2answers
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### Prove that L is a sub-language of the CFG G by using induction. (CFG,Induction,School)

i am asking for help with a question from a course in Logic im reading at university. I am aware that this type of question is frequently asked here(i have looked at alot of other questions/answers) ...
3answers
103 views

### Prove that there is no largest irrational number

I have to prove that there is no largest irrational number from the result of the a previous proof: Prove that if $x$ is rational and $y$ is irrational then, $x+y$ is irrational. I was able to prove ...
1answer
21 views

### How to show if two polynomials are equal for all substituted real numbers, then all the coefficients are equal

Let $p(x)=c_0+c_1x+\ldots+c_lx^l$ and $q(x)=d_0+d_1x+\ldots+d_mx^m$ be polynomials with real coefficients. Suppose $\forall x\in\mathbb{R}$, $p(x)=q(x)$. Show that $l=m$ and that for all $i=0,\ldots,l$...
1answer
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### Would this be considered a valid proof for $\forall r \in R$ if $0 < r < 1$, then $\frac{1}{r(1-r)}\geq 4$

I did a proof of the following $\forall r \in R$ if $0 < r < 1$, then $\frac{1}{r(1-r)}\geq 4$ using a proof by contra-positive, which was different from the direct proof that the solutions ...
0answers
235 views

### Theoretical proof of convergence of sequential weight update procedure (Neural Networks and Machine Learning)

My question is at the bottom. (Most of the descriptive words come from Chris. Bishop's Neural Networks for Pattern Recognition) Let $w$ be the weight vector of the neural network and $E$ the error ...
0answers
27 views

### Uniqueness of sum and multiplication of numbers

so I was writing a program that took two strings and said if they were anagrams or not, and I had this idea of making each character into a number, adding them all and checking if the result was the ...
2answers
52 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 ...
1answer
15 views