Define a mamzer

Question:

1. Is the offspring of a single Jewish woman and a single Jewish man, who do not get married, a mamzer?
2. Is the offspring of a single Jewish woman and a single non-Jewish woman, who do not get married, a mamzer?

Answer:

1. No however the child would be considered a pakum, since his mother most probably was a nidah at the time.
2. Nature doesn’t allow this.