SOLUTION: Can a function be continuous at one value of x and discontinuous at all other x E R? Explain your answer, giving proofs where appropriate.

SOLUTION: Can a function be continuous at one value of x and discontinuous at all other x E R? Explain your answer, giving proofs where appropriate.

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Question 549996: Can a function be continuous at one value of x and discontinuous at all other
x E R? Explain your answer, giving proofs where appropriate.

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
No. If f is continuous at x and only x, then for any x-values arbitrarily close to x, f must also be continuous (since continuity is defined using the limit as x approaches a fixed number), so we have a contradiction.
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