Using a word like "definition" when you're making shit up, doesn't make it true. If you say "Definition" - use a dictionary. For example, your definition of "republic means there's no king" - is hilarious, I actually feel bad for you. The actual definition of Republic is: a state in which supreme power is held by the people and their elected representatives, and which has an elected or nominated president rather than a monarch.
For example, rule by the people (the actual meaning of the greek demos and kratos). We are NOT, however, ruled by the people - we are governed by elected representatives (republic). The people do not make legislation, the representatives do.