Proving 3/4 is Infimum of A: A = { x^2 +x + 1 }

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To prove that 3/4 is the infimum of the set A = {x^2 + x + 1}, one must show that for any M < 3/4, there exists an x such that x^2 + x + 1 > M. The discussion highlights the need for clarity in assumptions, specifically that x is a real number and the correct inequality should be x^2 + x + 1 ≤ M. Completing the square is suggested as a method to derive the necessary proof. The thread emphasizes the importance of correctly categorizing the problem as mathematical rather than physics-related.
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Homework Statement



Giva a formal proof that 3/4 is the infimum of the set : A = { x^2 +x + 1 }

Homework Equations


I need a clear way to prove it - to understand the contradiction.


The Attempt at a Solution


I've assumed there is a M<3/4 that x^2 +x + 1>M. where is the contradiction?
 
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I've assumed there is a M<3/4 that x^2 +x + 1>M
I think you mean ##x^2 +x + 1\leq M##? Otherwise it would be a bit pointless.

You should have given ##x \in R## somewhere.
 
Why is this posted under "physics"? It is clearly a math problem- complete the square.
 
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