Proving a formula ∀x:x∈A∧|x−1|<a⟹x=1

[solakis1]

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

$$\forall x$$:$$x\in A \wedge |x-1|<a\Longrightarrow x=1$$

 

[Evgeny.Makarov]

It is not clear from the statement if $A=\{1,2\}$. Also, what set does $a$ come from?

 

[solakis1]

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]

 

[Evgeny.Makarov]

Spoiler

Then one can take $a=1/2$.