For posts seeking explanation or clarification of a specific step in a proof. "Please explain this proof" is off topic (too broad, missing context). Instead, the question must identify precisely which step in the proof requires explanation, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplicate questions.
Questions tagged [proof-explanation]
11824 questions
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Proof that every codeword of binary self-orthogonal linear code has even weight
A linear code $C$ is self-orthogonal if it is contained in its dual code, that is $C\subseteq C^{\perp}$
I want to proof that every codeword of $C$ has even weight
What I got by far:
Supposing that $C$ is a binary linear code, I can consider $x\in…
E. Williams
- 161
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Rudin Theorem 1:11: understanding why $L \subset S$
Rudin's theorem 1.11 states:
Suppose $S$ is an ordered set with the least-upper-bound property, $B \subset S$, $B$ is not empty, and $B$ is bounded below. Let $L$ be the set of all lower bounds of $B$. Then $\alpha = \sup L$ exists in $S$, and…
John P.
- 2,136
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Why does $g^p = mN + 1$?
In this video https://www.youtube.com/watch?v=lvTqbM5Dq4Q at 5:20, he says that: If you have a number, $N$, and a smaller number that is not a factor, $g$, you can raise $g$ to some power, $p$, so that it is equal to a multiple of $N$ plus one.
$g^p…
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Understanding transitivity of set elements
The following is a very simple exericse in Rudin.
Let $E$ be a nonempty subset of an ordered set; suppose $\alpha$ is a lower bound of $E$ and $\beta$ is an upper bound of $E$. Prove that $\alpha \leq \beta$.
The proof goes something like this.…
John P.
- 2,136
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Question on proof that $\sqrt{2}$ is irrational
The standard proof that $\sqrt{2}$ is irrational (for example, the one in Baby Rudin) says that, upon assuming for a contradiction that $\sqrt{2}$ is rational, that we can write $\sqrt{2} = \frac{p}{q}$ where $p$ and $q$ "have no common factors."…
John P.
- 2,136
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Prove: $ x + 9/x \geq 6$ for every positive real number $x$
I’m at a loss as to how to prove this. I thought it would be a good idea to use a Direct Proof to tackle this problem, and thus solved it algebraically, but upon revising, the “for every positive real number x” confused me.
I revised my textbook…
Julius Pepus
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Why is $x$ divided by $n$ the same as $1$ divided by $n$ times $x$?
I'm very new here and my question must have been answered before, but I don't know how to search this site with problems like mine.
My question is why $x/n$ is the same as $1/n*x$?
Also, if you don't mind, tell me how to search this site effectively…
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Prove or disprove: there exists $a ∈ \Bbb N$ such that for all $n ∈ \Bbb N$, $an + 1$ is prime.
I'm trying to do this homework problem that states the following:
Prove or disprove: there exists $a \in \Bbb N$ such that for all $n \in \Bbb N$, $an + 1$ is prime.
I tried splitting it into cases based on the parity of $a$ and $n$ but so far all…
nicons
- 63
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Proofs a logical form
Let $\mathcal F$ be a non-empty family of sets with $A\in\mathcal F$.
$(a)$ Prove $A\subset\bigcup\mathcal F$
$(b)$ Prove $\cap\mathcal F\subset A$
$(c)$ Why was the assumption that $\mathcal F$ is nonempty needed?
Was it needed for both parts…
Kuan N
- 31
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Elliptic integral and AGM
I need help, I'm looking at Elliptic integrals and why you can use AGM to compute it. I got the point why, but I didn't understand some steps where Gauss make a proof on it. He came with new variable $\varphi'$, where
$\sin(\varphi) =…
MathIsFun
- 11
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3 answers
Prove that $f(x) = x^3+x^2$ is surjective.
Let $f$: $\mathbb{R}$ to $\mathbb{R}$ defined by $f(x) = x^3+x^2$. Prove that $f(x)$ is a surjective function.
I'm not quite sure how to approach this problem. If the function had an inverse, I could show that it would be bijective and therefore…
user693580
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How to prove $A$ is equivalent to $B$?
I know that to prove $A$ is equivalent to $B$, I have to assume $A$ then prove $B$ and then assume $B$ and prove $A$. But let’s say that $C$ is a axiom. Can I use $C$ in my proof of $B$ from $A$ and vice versa? Or can I only use $A$ and $B$, and not…
phst
- 586
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Why does x > a in this proof?
The proof for Theorem 13.9 from "Introduction to Metric & Topological Spaces" by Wilson Sutherland.
The definition for compact is that any open cover can be reduced to a finite open cover for a compact…
HF_
- 28
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Prove that $\sim$ is an equivalence relation on $\mathcal{P}(X)$
Given $X$ a non-empty set and $\mathcal{P}(X)$ with relation $\sim$ on $\mathcal{P}(X)$:
$$\forall A, B \subset X: A \sim B \Leftrightarrow A \Delta B \text{ is finite}$$
Prove that $\sim$ is an equivalence relation on $\mathcal{P}(X)$.
I know…
NimaJan
- 290
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Show $A\cup B$ is denumerable by constructing a bijection
I just need some clarifications in the solution to the problem my teacher gave me below:
Suppose A and B are disjoint denumerable sets. Show that $A\cup B$ is denumerable by constructing a bijection.
proof: Since A and B are denumerable, then…
Jr194
- 109