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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How do we prove the statement $x^{2} \geq 36$ implies $|x| \geq 6$ by contradiction?
Proof by contradiction seems to confuse me and I need help with this specific question.
In particular, how do we prove the following statement by contradiction:
If $x^2 \geq 36$ then $|x|\geq 6$ (?)
HannahJ
- 29
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2 answers
How to prove $\frac{1}{\sqrt{a} + \sqrt{b}} = \sqrt{a} - \sqrt{b}$?
My daughter is learning how to rationalise surds for her school exams. One example being worked through is the following:
$\frac{1}{\sqrt{6} + \sqrt{5}}$
In the tutorials she is following, the first step is rearranging to arrive at:
$\sqrt{6} -…
Chris Snow
- 237
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1 answer
Could someone explain the proof of this theorem to me?
enter image description hereHello, I’m new to math and I consider myself a hobbyist. Could someone explain the type of proof this is and how it works? I can see that it appeared to be a proof by contradiction but I don’t understand where the…
Michael Bradley
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3 answers
Proof of why $\sqrt{2}$ is an irrational number
I am studying the proof by contradiction below. But I am confused on why the proof is valid. It first assumes that $p, q$ have no common factor, and then arrives at a conclusion where $p, q$ are both divisible by $2$, and hence they do have a common…
student010101
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1 answer
Prove function is greater than or equal to 0
Let $f(x)=x^4-2x^3+3x^2-2x+1$. Prove that $f(x) \ge 0$ .
My thought is I need factor the function into sum or difference of perfect squares to show it's always non-negative. Any suggestions?
Drake
- 851
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votes
2 answers
$a^2 |b$ and $b^3 |c$ , prove $a^6 |c$
Suppose $a$, $b$, $c$ ∈ Z. If $a^2 |b$ and $b^3 |c$ , prove $a^6 |c$
I have been asked this question, and am unsure how to solve. I have tried to equate $b = ma^2$ , but may have done this wrong.
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proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
The proof that shows the square root of 2 is irrational starts by assuming, for a contradiction, that it is rational. It starts with the assumption that it can be written as p/q where p and q have no factors in common.
Why do we start by assuming p…
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3 answers
Prove irrational
Prove that $\dfrac{1+\sqrt{5}}{2}$ is irrational.
a.)Without assuming $\sqrt{5}$ is irrational.
b.)With assuming $\sqrt{5}$ is irrational.
For a.) would I just do a proof by contradiction. Assuming that the entire expression is rational?
tskgreen
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2 answers
Find what is wrong with this proof:
$a = b$
$a^2 = ab$
$a^2 + a^2 = a^2 + ab$
$2a^2 = a^2 + ab$
$2a^2 - 2ab = a^2 + ab - 2ab$
$2a^2 - 2ab = a^2 - ab$
$2(a^2 - ab) = 1(a^2 - ab)$
$2 = 1$
What is the error in this proof??
Bebuji
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1 answer
Domination proof
eventually dominated(ed) $\exists m \in \mathbb{R}_{\ge 0}: \forall n \in \mathbb{N}, n \ge m \Rightarrow g(n) \leq f(n)$
$\forall x, y \in \mathbb{R}_{\ge 0}, g(n) = xn + y$ is (ed) by $f(n) = n^2$
Should translate to..
$\forall…
shibu
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1 answer
Proof that 8 is an even number by using contradiction technique
My tutor gave an online assignment with this question:
Proof that 8 is an even number by using contradiction technique
I've read about Proof by contradiction but I couldn't come up with any idea on how to start solving this.
Any help is much…
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2 answers
Explain the proof of irrationality of $\sqrt{2}$
How does this proof show the irrationality of $\sqrt{2}$ ?
I am new to proofs and don't really understand the logic used here.
yung sprint
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2 answers
Prove that for every three sets A, B, and C we have (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C).
I need help solving this question. I understand that we need to prove that the LHS is a subset of the RHS and that the RHS is a subset of the LHS, but I don't really know what to do afterwards.
CodingKook
- 23
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1 answer
Proof system soundness and completeness
Is a proof system with the single rule of inference {}⊢ φ for all φ sound, complete, both, or neither?
I think it is sound but I feel like there is a caveat, am I wrong?
Dezmond
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1 answer
Proofs Involving Real Numbers question
my question is about Proofs Involving Real Numbers
which is :
Let $x,y ∈ \Bbb R$, prove that if $x<0 $, then $x^3-x^2y \le x^2y-xy^2$
