There are two definitions(do bear in mind you're using wikiPlease Register or Log in to view the hidden image!). The second one there isn't very detailed, but it is edging towards the correct one for most atheists. Not so much rejecting but lacking a belief in god. Obviously stating clearly god does not exist is a belief as you cannot prove the non-existence of anything unless it has clearly defined parameters. So if someone said god was on my bed, I can look and see clearly god is not, hence it's non-existence can be proven. However if they say he is invisible and cannot be touched I cannot prove his non-existence, but without proof he is there(beyond hearsay) I will still lack a belief in his existence, this makes me atheist by default as you either believe or lack that belief(note I wouldn't be saying he is not/cannot be there). Agnosticism is attributed to knowledge, so you can say I believe in god but am aware I cannot prove said belief, or I lack belief but given the parameters I cannot prove non-existence. Hence agnostic atheists and agnostic theists, she's halfway there but missing very important bits of information. I'm sure you can understand this. I may be wrong but it seems pure agnosticism is actually impossible. I wouldn't really attribute coolness to any of it, you just find what is right for you, you can be agnostic atheist if you like.