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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1 answer
The Equation of The Phantom Traffic Jam
I am currently reading a lot of essay about traffic to help my term paper. I have came across lots of equations including the popular ones. On a site, I found an equation that is the most relevant to me but in the site there were no derivation which…
kymbl
- 11
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1 answer
Number of representations of numbers in a given radix
I came across this question recently: Prove that there is only one unique base b representation of any natural number.
It states that in any base >= 2, there is only one representation of any given integer. But, I thought of using 10 as b and 2 as N…
Jigsaw
- 497
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0 answers
What is the proof for the existence of fractional exponents?
I've been thinking about this for a while; and I'm pretty sure I've seen most of the text book explanations for it that are out there. I've found that, the explanations are pretty much all the same; they all use the same principle, the most basic of…
Amin Parvaresh
- 439
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0 answers
Mathematical Techniques When Proving Compton Scattering
When attempting to prove the formula for Compton Scattering, I obtained the following equation(I have omitted the details on how the equation is obtained as it is not relevant to this post):
$$f = f' + k(f^2 - 2ff'\cos\theta +f'^2)$$
where $~k~$ is…
Yiyang Zhi
- 21
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2 answers
Proving similarity of triangles in the power of point theorem.
Maybe I’m missing something obvious, but why can we say:
Angle BCD = (arc BD)/2?
Similarly why can we say:
Angle ABD = (arc BD)/2?
This is a step in part of a proof for the power of a point theorem (specifically trying to prove that triangle ADB is…
Jamminermit
- 1,923
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simple proof confusion composite and prime
if m>n>0, is m^2 - n^2 composite?
p is composite if p>1 and there exists positive integers r & s such that p = rs where 1< r < p and 1
m^2 - n^2= (m+n)(m-n)
let m =2 and n =1
let p = m^2 - n^2
p = 3 or (3)(1)
let r = (m+n) and s = (m-n)
r…
Ryan gomez
- 45
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1 answer
Proving a sine-function is surjective
$f: \mathbb{R} \to (-\infty, 4]$
$f(x) =-\frac {sin(\frac {11x\pi}{6})}{5}+2$
I don't quite understand how to prove that this is a surjective function. I know that all values of x are mapped to at least one value of y in the given co-domain. From…
Bullerskydd
- 39
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1 answer
Can anyone elucidate vague hint towards the contradiction of $x^{-1}*x=1$ and $x*0=0$ in $x\in R/0$ $ \implies$ $x^{-1}\in R/0$ in an author's proof?
For any $x \in R$
$$x\cdot 0 = 0\cdot x =0$$
Proof:
$$x\cdot 0=x\cdot (0+0)=x\cdot 0+x\cdot 0 \implies x\cdot 0=x\cdot 0+(-(x\cdot 0))=0$$
▸ From here, by the way, it can be observed that if $x\in R\setminus 0$, then $x^{-1}\in R\setminus 0$
How…
Misha.P
- 221
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What does $*$ mean in equivalence relations?
The notation of "$*$" started being used in my proof textbook in the section of equivalence relations and partitions yet it never once said what it means.
An example from the textbook:
Let $\mathbb{Z}^* = \mathbb{Z} - \{0\}.$ Define the relation…
David
- 97
- 8
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Please help I'm in grade 9 and excellent at maths but I keep asking why does it work
Please help, i'm in grade 9 and get exellent maths grades and everyone regard me smart but I keep asking myself why does this work and it gets really bothering
Example when we studyed system of equations I start ask why does the substition method…
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2 answers
How do I prove that for any $y$ $\in$ $B$, $y$ $\in$ $f$($A$)?
In order to show (c), I know that I need to show that for every element, y $\in$ $B$, y $\in$ $f$($A$). I take $y$ to be arbitrary and show $y$ $\in$ $f$($A$) by showing it is in the universal set and that it satisfies the given condition. So, I…
KM9
- 135
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1 answer
A coloring of all plane points with coordinates belonging to the set $S = \{0, 1, . . . , 99\}$
A coloring of all plane points with coordinates belonging to the set $S =
\{0, 1, . . . , 99\}$ into red and white colors is said to be reddish if for each $i, j ∈ S$ at least
one of the four points $(i, j),(i + 1, j),(i, j + 1)$ and $(i + 1, j +…
nonuser
- 90,026
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0 answers
Clarification on the method used to prove the existence of $\sqrt{2}$ in $\mathbb{R}$
Let $A=\{x\in \mathbb{R}:x^2\leq{2}\}$ with $\sup A=\alpha$.
When proving that the $\sqrt{2}$ exists in $\mathbb{R}$ using the method of contradiction, do we show that a contradiction arises for the case $\alpha^2 \lt{2}$ by negating condition $1$…
user503154
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2 answers
2 has a square root in $\mathbb{R}$ - proof explanation
Can someone please help me to understand the steps of the proof below.
What do the assumptions become when we use the proof by contradiction in the cases where $s^2\gt{2}$ and $s^2\lt{2}$? Can you please state the theorem in the form of an "if...,…
user606466
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3 answers
Where is the mistake in this proof that "If the square of a number is even, then the number is even"?
The proof given in This question is incorrect (the proof will be posted at the end for convenience). However, the question seem to address the fact that the statement to be proven is not stated correctly, and not the fact the the proof is…
user106860
- 965