Blocking numbers on a cingular cell phone?

[Sonya Namour]

I have cingular/at&t phone service. i recently blocked the number of someone who has verizon service, it wasn't my choice or anything i could control. i am unsure if they know that they are blocked yet but i am wondering what will happen if they went to send me a text message or call me? would the text message not send? would they get a reply message back saying that their message couldn't be delivered even though they have verizon? would the call go through?
If anyone has experience blocking phone numbers on cingulars service it would be appreciated