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
2
votes
4 answers
I do not understand this particular step in a proof using the Well Ordering Principle
Below is a proof using the Well Ordering Principle. I get lost starting at $(13)$...
$$
\begin{aligned}
P(c): &:=c^{3} \leq 3^{c} \\
& \equiv c^{3} \leq 3(c-1)^{3} \\
& \equiv c \leq \sqrt[3]{3} \times(c-1)
\end{aligned}
$$
I don't understand how we…
Robert W
- 333
2
votes
3 answers
How do I prove that a set of all finite subsets of $\mathbb{N}$ is countable?
Let $X$ be the set of all finite subsets of $\mathbb{N}$. Thus some elements of $X$ include $\emptyset$ and $\{1, 5, 9\}$ and $\{3, 346\}$ and $\{1\}$; however, the set of even natural numbers is not an element of $X$. Prove that $X$ is countable.
I…
Q G
- 21
2
votes
1 answer
Some obscure points about the proof of Hahn Decomposition Theorem
The Hahn Decomposition Theorem. If $\nu$ is a signed measure on $(X,\mathcal{A})$, there exist a >positive set $P$ and a negative set $N$ for $\nu$ such that $P\cup N=X$ and $P\cap N=\emptyset.$
Proof Without loss of generality, we assume that…
Jack J.
- 920
2
votes
1 answer
$\displaystyle{\limsup_{x \to \infty} f(x) = L = \liminf_{x \to \infty} f(x)}$ proof
In the following link at the end of the page there is presented a proof for the following theorem:
Let $f : (a, \infty) \to \mathbb{R}$ where $a \in \mathbb{R}$. Then
$\displaystyle{\lim_{x \to \infty} f(x) = L}$ if and only…
Michael Munta
- 175
2
votes
1 answer
Contrapositive/contradiction proofs and why do they work
Show that if x and y are two integers whose product is even, then at least one of the two
must be even (use the contrapositive argument)
now the thing is I understand how to prove this with a contrapositive argument and without. what I don't get is…
RandomGuy57
- 115
2
votes
1 answer
If we want to show something for every x, why do we...
If we want to show something for every $x \in X$ of, sometimes we simply say: Let $x$ be $\in$ of $X$ (x is arbitrary). And if we continue doing that,after the proof is done, this allows us to say that it holds $\forall x$. Why does it work ? I…
Maths
- 345
- 1
- 9
2
votes
1 answer
Derivation of 2D / binormal / bivariate Gaussian general equation
I am trying to understand how the general 2D Gaussian (binormal / bivariate) equation is derived as part of my work, and am having trouble expanding the terms. The article on Wikipedia…
2
votes
2 answers
Is this a typo in Section 1.8.1 Mathematics for Computer Science?
Am I completely mistake or is it suppose to say $n^2$ is a multiple of 2 and therefore $n$ must be a multiple of 4?
This is from MIT's Mathematics for Computer Science
doctopus
- 491
2
votes
2 answers
Confusion regarding the completeness axiom
Why would we use square root of 2 in our example to show that the rationals don't have a supremum when square root of 2 is not an element of the rationals? Wouldnt the supremum be the element of the rationals that is greater square root 2 or less…
user503154
2
votes
5 answers
Prove that if $|x|<1$ then $x^{6}<1$
I am trying to prove that if $|x|<1$ then $x^{6}<1$ and that if $x^{6}<1$ then $|x|<1$.
For the first part, I thought of first considering $0
JennyToy
- 385
2
votes
2 answers
Explanation of proof by contradiction
There's one part of an explanation of proof by contradiction that I don't understand at the moment.
Here's the explanation:
"Let's say we desire to prove the truth of a statement,M.
A proof by contradiction will proceed by initially assuming that M…
stochasticmrfox
- 909
2
votes
2 answers
Number bases $p$
I did not understand the proof of this lemma, could anyone help me?
Lemma.
Let $p\in\mathbb{N}$, $p\ge2$. Let $x\in[0,1)$ such that
\begin{equation}
x=\sum_{k=1}^{\infty}\frac{a_k}{p^k}=\sum_{k=1}^{\infty}\frac{b_k}{p^k}
\end{equation}
with…
Jack J.
- 920
2
votes
2 answers
Proof check modulo arithmetic
what is wrong with this proof,
so I am supposed to show $7x^2-15y^2=1$ has no integer solutions...
so since $7x^2=1+3(5y^2)$ so $7x^2\equiv 1 \pmod{3}$
hence in mod $3$, $x\equiv 0, 1$ or $2$ so $x^2\equiv 0, 1$ and $7x^2\equiv0$ or $7$
and since…
user523955
2
votes
2 answers
Proof of rule for multiplying numbers with uncertainties
So suppose you have a value $A$ with an absolute uncertainty $\pm a$ and another value $B$ with absolute uncertainty $b$, it is easy to prove that the rule for dealing with the uncertainties when adding these values like so:
$$(A\pm a)+(B\pm…
cal
- 65
2
votes
3 answers
Where is the mistake in the induction proof for 'All horses are the same color'?
I don't really understand Wikipedia's proof, because 1. if we assign distinct numbering to all the horses, I find obvious that there can be common elements to two subsets.
Also, is the mistake in the initial assumption ($n$ horses always have the…
JobHunter69
- 3,355