Are bananas infinite?

I was sitting on the couch, eating a banana. And Delicia was sitting next to me.
- You want some? I asked her.
- Yeah, she said.
I gave her the banana and she took a bite. Actually I didn’t give her the banana, I only held it so she could bite. And she bit. And then I bit.
- You want some? I asked her.
- Yeah, she said.
There was only a little piece of banana remaining. Delicia bit half of what was left. And then I bit.
- You want some? I asked her again.
- Yeah, she said.
And bit half of what was left. Then I bit half of what was left.
- You want some?