How is continuity of a constant function defined?

Question

• Definition of continuity is that for small changes in the input there should be small changes in the output.Otherwise the function is discontinuous.

  So,with this definition we can say that a constant function is discontinuous.

• Another definition for continuity is that: "L.H.L = R.H.L = value of function at that point"

  with this definition we can say that constant function is continuous .

So,why am I facing a contradiction ,I wonder if my understanding is wrong about the continuity of a function.

Answer 1

Your first definition is wrong. It should read:

for small changes in the input there should not be large changes in the output. Otherwise the function is discontinuous.

No change is not a large change (which is what Cameron essentially said in jest in his comment).