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 $a=1/2$.
 

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