# Tagged Questions

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

1answer
65 views

### proof of Triangle Removal Lemma

Where can I find a proof of the following version of Triangle Removal Lemma (or any version equal to it)? Let $G(V,E)$ be a graph on $n$ vertices such that it contains $\varepsilon n^3$ triangles, ...
1answer
14 views

### If unions of two families sets are disjoint then families of sets are disjoint too.

I have read that theorem "Suppose $\mathcal{F}$ and $\mathcal{G}$ are families of sets. If $\cup\mathcal{F}$ and $\cup\mathcal{G}$ are disjoint, the so are $\mathcal{F}$ and $\mathcal{G}$" is ...
2answers
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3answers
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2answers
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2answers
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### My proof that $f[f^{-1}(D)] \subseteq D.$

I've just started studying formal proof and set theory, so it'll be really cool if someone can check out my proof for a pretty basic set theory problem. It'll be great if you can tell me if my proof ...
1answer
30 views

2answers
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### Proving by contradiction (6/9)

I have been given a statement that I need to prove using the contradiction method and I am just a little unsure of how to go about setting this up and executing. Here is the statement: If x is any ...
3answers
45 views

### Show that the closure of $A$ is the intersection of all closed sets containing $A$, topology proof needed

I want to show that given $(X, \mathcal{T})$, we define $\overline A = \{x \in X| \forall U \in \mathcal{T}, x \in U \implies U \cap A \neq \varnothing\}$ (definition of closure from Munkres), then ...
0answers
13 views

### Proof Function is Bounded/Unbounded

How can I prove that the function $$\sigma_i\left(t\right) = k_i\left[\left(a+b\left(T_i-t\right)\right)e^{-c\left(T_i-t\right)}+d\right]$$ is bounded/unbounded? Note: $\sigma_i\left(t\right)$ is ...
0answers
36 views

### Which is finer, co-countable topology or usual topology on $\mathbb{R}$?

We know that the usual topology is finer than co-finite topology on $\mathbb{R}$ How to show the usual topology is finer than co-finite topology on $\mathbb{R}$ And co-countable topology is (in ...
3answers
176 views

### How to integrate $\int_{-3}^3 (x^2-3)^{3} \,dx$ without expanding the polynomial?

How can I integrate: $$\int_{-3}^3 (x^2-3)^{3} \,dx,$$ neither expanding the polynomial nor using the relationship between integral and derivatives? I mean, there is a way to compute this integral ...
4answers
87 views

### Proof writing: $\sum_{n=1}^{\infty}| a_n|<\infty$ implies $\sum_{n=1}^{\infty} a_n^2<\infty$.

Let $\sum_{n=1}^{\infty} a_n$ be an absolutely converging series. By definition, this means $\sum_{n=1}^{\infty} \lvert a_n\rvert$ converges. We want to show that $\sum_{n=1}^{\infty} a^2_n$ ...