# Support Vector Classifier and cost C

Applying SVC (Support Vector Classifier) to the 1-d data shown here:

What will be the support vectors for the parameter cost C=0 and C=Infinity?

As far as I read about SVM and hyper parameter C I would say:

For C = 0 there will be no support vectors

For C = Infinity all of the data points will be support vectors

Is it correct? Note that I'm talking about SVC not SVM