# Questions tagged [proof-writing]

For questions about the formulation of a proof. This tag should not be the only tag for a question and should not be used to ask for a proof of a statement.

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### Proof verification of exercise 7(a), section 31 of Munkres’ topology

Let $p \colon X \rightarrow Y$ be a closed continuous surjective map such that $p^{-1}\big(\{ y \} \big)$ is compact for each $y \in Y$. (Such a map is called a perfect map.) (a) Show that if $X$ is ...
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### What are some strategies to write a proof that can be easily comprehended?

There are already a lot of articles on how to correctly write a proof. In contrast, assuming that I already have a very hard proof written, I am interested in rewriting the proof to make it easy to ...
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### Exercise 7(c), Section 31 of Munkres’ Topology

Let $p \colon X \rightarrow Y$ be a closed continuous surjective map such that $p^{-1} \big( \{ y \} \big)$ is compact for each $y \in Y$. (Such a map is called a perfect map.) (c) Show that if $X$ is ...
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### If I define addition in the following way, how can I prove that it's commutative?

$a+b=a$, if $b=0$ $a+b=S(a)+S^{-1}(b)$, if $b\not=0$ Here a and b are natural numbers defined according to the Peano axioms, while S represents the successor function. Basically, I am trying to prove ...
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### Exercise 7(b), Section 31 of Munkres’ Topology

Let $p \colon X \rightarrow Y$ be a closed continuous surjective map such that $p^{-1} \big( \{ y \} \big)$ is compact for each $y \in Y$. (Such a map is called a perfect map.) (b) Show that if $X$ is ...
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### Exercise 7(a), Section 31 of Munkres’ Topology

Let $p \colon X \rightarrow Y$ be a closed continuous surjective map such that $p^{-1}\big(\{ y \} \big)$ is compact for each $y \in Y$. (Such a map is called a perfect map.) (a) Show that if $X$ is ...
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### For which values of $n$ does there exist $n$ real $n\times n$ matrices $A_1,\cdots,A_n$ such that $A_1v,\cdots,A_nv$ are always linearly independent? [duplicate]

Here's a question that I have been stuck trying to figure out the right answer AND write a vigorous proof for weeks. Here's the question: For which values of $n$ does there exists $n$ real $n\times n$ ...
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### How do I prove formally that for all natural numbers $a\cdot S(c)=b\cdot S(c)\implies a\cdot c=b\cdot c$

Natural numbers, addition, multiplication, and the successor function S, are defined in the wikipedia article regarding Peano axioms. https://en.m.wikipedia.org/wiki/Peano_axioms Originally I was ...
### For all natural numbers $n$, if $n$ is odd, then $\sqrt{15^n}$ is irrational.
How can I show that for all natural numbers $n$, if $n$ is odd, then $\sqrt{15^n}$ is irrational? I have tried to use a proof by contradiction to no avail. I have gotten decently far with a proof by ... 