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 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

I Proving Newton's forward difference interpolation formula
Replies
1
Views
311
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 Rational Number: Proving $x+\dfrac{1}{x}$ is Rational
Replies
1
Views
973
I Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
Replies
16
Views
585
MHB Prove Root of Polynomial $P(x)=x^{13}+x^7-x-1$ Has 1 Positive Zero
Replies
2
Views
1K
MHB Proving $x-1$ is a Factor of $P(x)$ with Polynomials
Replies
1
Views
1K
MHB Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top