MHB Proving a formula ∀x:x∈A∧|x−1|<a⟹x=1

  • Thread starter Thread starter solakis1
  • Start date Start date
  • Tags Tags
    Formula
AI Thread Summary
The discussion centers on proving the formula that for the set A = {1, 2}, there exists a real number a > 0 such that for all x in A, if the absolute difference |x - 1| is less than a, then x must equal 1. Participants express confusion regarding the definition of the set A and the origin of the variable a. Clarification is provided that A is indeed {1, 2} and a is a real number. The focus remains on establishing the conditions under which the formula holds true. The conversation emphasizes the need for precise definitions in mathematical proofs.
solakis1
Messages
407
Reaction score
0
Given the set {1,2},prove that there axists an a>0 such that:

$$\forall x$$:$$x\in A \wedge |x-1|<a\Longrightarrow x=1$$
 
Last edited:
Mathematics news on Phys.org
It is not clear from the statement if $A=\{1,2\}$. Also, what set does $a$ come from?
 
Evgeny.Makarov said:
It is not clear from the statement if $A=\{1,2\}$. Also, what set does $a$ come from?
[sp]Sorry, A={1,2} and a is a real No [/sp]
 
Then one can take $a=1/2$.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

MHB Equation 2: Prove that ##x^2+2x\sqrt x+3x+2\sqrt x+1=0##
Replies
4
Views
1K
I Calculating the root of a number by hand
Replies
6
Views
2K
MHB Is this Trigonometric Expression a Constant Function of x?
Replies
2
Views
1K
MHB Proving Equivalence of f(x) and g(x)
Replies
5
Views
1K
MHB Proving the Equality of A and B: A+B=0 or A=B
Replies
2
Views
1K
MHB Rational Number: Proving $x+\dfrac{1}{x}$ is Rational
Replies
1
Views
940
MHB Prove Root of Polynomial $P(x)=x^{13}+x^7-x-1$ Has 1 Positive Zero
Replies
2
Views
1K
MHB Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?
Replies
2
Views
1K
MHB Proving $x-1$ is a Factor of $P(x)$ with Polynomials
Replies
1
Views
1K
I Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
Replies
16
Views
456

Hot Threads

Recent Insights

Back
Top