can you block a phone number without the person that owns the phone knowing?

Some phone companies will say you are not accepting calls. Others just automatically send them to voice mail. When a call goes direct to voice mail like that and then always and every time it goes straight to voice mail, then the caller begins to wake up to the idea that you don't want to talk.

Well on most cell phones It will not say blocked the call just will not go through and im almost positive it is the same with landlines so as long as there is not a reject list option to look up on the phone than it will not be visible and will not show the call 10 points please

It is a home phone, so there for they cannot tell. Even if it was another phone, they could not tell.

If it is a BT land line just ring BT and they will sort it for you.