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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What is the logical justification for proof by contradiction?
A book I'm reading states that when constructing a proof by contradiction we create the conditional ¬R ⟹ C, where R is the statement we are trying to prove, and C is the contradiction. To explain why R must be true, it says that C is considered…
IgnorantCuriosity
- 1,423
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3 answers
Does proof by contrapositive take into account that P might be false regardless of whether we have Q or not Q?
It seems that proof by contrapositive only counts as a proof because it assumes a connection between P and Q. For example, say we have the statement: If unicorns exist, then it is raining. If we wanted to prove this using proof by contrapositive, we…
IgnorantCuriosity
- 1,423
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3 answers
Alternative perspective on mean value theorem in one-dimensional space
In my textbook, there is an alternative perspective on the mean value theorem that I don't understand. When we introduced the mean value theorem the first time, the statement looked like…
Julian
- 1,401
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0 answers
How does the division theorem hold if $a
My understanding of the division theorem:
Let $a,b$ be integers, $b>0$. Then there are unique integers q,r such that $a=qb+r$, and $0\leq r
IgnorantCuriosity
- 1,423
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votes
1 answer
Why is "To prove P, assume ∼P and arrive at a false statement, which would make P true" an inaccurate description of proof by contradicition?
I have a quiz with the following question:
Which of the following describes proof by contradiction?
D) To prove P, assume that ∼P is true and arrive at a false statement, thus proving ∼P would also be false, which would make P true.
D) isn't the…
Charles Clayton
- 109
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5 answers
Proof of inequality using AM-GM inequality
prove that $x^2 + y^2 + z^2 \ge xy + xz + yz$
I tried proving it the way I prove $x^2 + y^2 \ge 2xy$. But it just doesn't seem to work. I tried using AM-GM. Should I be using GM-HM or AM-HM? I really don't know what the problem is and I'd appreciate…
user346756
- 293
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0 answers
Intuition/Clarification of Surface of Revolution Proof
In a lot of math formulas, I usually try to derive the formula by trying to reach rough approximation of the equation before looking at the actual equation itself (nearly 99% of the time I never get the equation but I get an idea).
For the surface…
Ian L
- 889
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1 answer
Proof that there are infinitely many sin values
Prove that there are infinitely many $n\in\mathbb{N}$ such that $sin(n)>\frac{1}{2}$ and infinitely many $n\in\mathbb{N}$ such that $sin(n)<\frac{-1}{2}$.
Seems so simple and probably is but I'm having difficulty proving this. Proof by contradiction…
Hasan
- 1
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Proof explanation of $[0,1]$ is compact
Let $X=[0,1]$. Prove $X$ is compact.
Let $\{U_i\}_{i\in I}$ be an open cover of $X$, or equivalently $$X=\bigcup_{i\in I} U_i~\text{and each}~ U_i~\text{is a open subset of}~X.$$
By definition of compactness we need to show that every open cover of…
johnny09
- 1,535
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1 answer
Simple proofs module
Let S be a set of three distinct integers. A be a nonempty subset of S and $\sigma _A$ be the sum of A.
Now prove that there exist two distinct non empty subsets $B,C\subset S$ with $\sigma _B\equiv \sigma_C \bmod 6$
Now I am able to figure out…
ALEXANDER
- 2,099
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3 answers
How to prove that $\frac{1}{9}= \sum_{i = 1}^{ \infty } \frac{1}{10^i}$
I am new here and I am eager to find out how to prove this:
$\frac{1}{9}= \sum_{i = 1}^{ \infty } \frac{1}{10^i}$
Is induction a method in order to prove that?
Even though, to my knowledge, induction only works for finite numbers.
I really want to…
OpenHax
- 3
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3 answers
Alternative proof for the irrationality of $\sqrt{2}$; questions
So I started reading Conjecture and Proof by Miklos Laczkovich and one of the first proofs he provides is that of the irrationality of the square root of two. I am aware there are alternative proofs (one of which is geometric and another that uses…
SelfStudy
- 767
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1 answer
How do i prove that a polynomial is factorable with real numbers only if the $b^2 - 4ac \geq 0$ using proofs.
Let $P(x)=ax^2+bx+c$
with $a≠0$
. The polynomial $P(x)$
is factorable in real numbers if we can find real numbers $m$
, $n$
, $k$
and $l$
so that $P(x)=(mx+n)(kx+l)$
.
a) Show that $P(x)$
is factorable if and only if $b^2−4ac≥0$
.
b) Show that…
-1
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1 answer
Proof that Conway's Game of Life's outcome is impossible to calculate
I know that it is impossible to know whether or not a starting pattern for the Game of Life will exist/destroy itself as iterations approach infinity. However, I haven't seen a proof of this. What is the proof of this claim?
Ben A.
- 101
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1 answer
Rudin Exercise 2.2: Proving the Hint
Rudin's exercise 2.2 asks for a proof that the set of all algebraic numbers are countable. I'm trying to understand a proof of this, which uses his hint. The first step proceeds as follow.
For each $N$, let $E_N$ denote the set of equations $a_0…
