Artful Dodger: Is the banana a fruit or a veggy..

I'm trying to figure this one out which without googling it. I think fruits have the seeds on the inside of the fruit itself, and veggies have their seeds somewhere else. The carrot makes its seeds up on the green part.. not sure, but I think that's right. Same with radishes. I remember having a garden with carrots and radishes once, but neglected it. I think eventually they both produced seeds up on the leafy part of the plant. The potato has its seeds on the skin.. again, I'm not sure but that seems right. The "eyes" of the potato (on the skin) are the seeds, aren't they?

So I'm going to say that fruits have their seeds inside of the fruit itself, while vegetables and grasses produce the seeds on the leafy parts of the plant.. or on the outside of the 'meaty' part of the plant. So that would make the banana a fruit.. ???

What about coconuts?