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

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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.
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Given the set {1,2},prove that there axists an a>0 such that:

$$\forall x$$:$$x\in A \wedge |x-1|<a\Longrightarrow x=1$$
 
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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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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