# Tagged Questions

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

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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 ...
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I've been stuck on this question for quite a while and I would appreciate if someone could help me out. A is regular open iff $A=A^{{\bot\bot}}$ where $A^{\bot}$ = X - $\overline{A}$. $A^{\bot} = ... 1answer 40 views ### Proof that$a^x$goes towards infinity as x goes towards infinity I'm tasked to prove that$a^x \rightarrow \infty $when$x \rightarrow \infty$provided that (a > 1). I've found a very rigorous proof for this. But my question is, why can't it be logically realized ... 8answers 234 views ### Prove that$4$divides$3^{2m+1} - 3$Prove that$4$divides$3^{2m+1} - 3$. By plugging in numbers I can see this is true, but I can't figure out a way to prove this, I was thinking maybe proving first that it is divisible by$2$, and ... 1answer 28 views ### How to show a continuous function from a space to a subspace is continuous from a space to the whole space? Let$(X,\mathcal{T})$and$(Y, \mathcal{J})$be topological spaces. Let$W \subset Y$be a subspace with its subspace topology. Show that if$f: X \to W$is a continuous function, then$f: X \to ...
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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $\sum_{n=1}^{\infty} a^2_n$ ...
### Show $\mathbb{N}^{\{0,1\}}$ is uncountable with a hint
Let $\mathbb{N}^{\{0,1\}} :=\{f: \mathbb{N} \to \{0,1\}\}$ is uncountable I have never heard of the table approach, and all the proofs say uncountability of $\mathcal {P}(\mathbb{N})$ I have seen so ...