Grafting bananas Stage II
 

Hello again Mauro! So, I wonder why the Brazilian bananeiros told you to cut off one of the wedded plants? It will be interesting to see this progress.
I enjoyed the videos, too. Was that a tree dahlia in the second video - it was in a photo just before the rice paddies. They are so beautiful!

Re: Grafting bananas Stage II
 

Oh not at all! Did you know there are objects with infinite length but only finite area? Consider the area between the x-axis and the curve e^(-x) from 1 to infinity ... :D

Re: Grafting bananas Stage II
 

Hey Mauro,

interesthing video again,can't wait till my pup's are big enough to
participait in this experiment.

grtz grad

Re: Grafting bananas Stage II
 

Wouldn't that still be an infinite area too, since the curve would approach, yet never touch the y axis? I mean it's been 35 years since college, so I may be rusty (okay, maybe more than rusty) but if the area is not enclosed, it cannot be measured finitely. As Dennis Miller says, "That's just my opinion, I could be wrong."
Now my brain hurts, thanks Richard.

Re: Grafting bananas Stage II
 

WOW!!! Being a total optimist... I lookd forward to furthere up dates ..I think it sounds very interestings and can't wait to see your results!! BTW WELCOME!! I look forward to seeing you around!
Kylie:waving:

Re: Grafting bananas Stage II
 

Welcome!

Re: Grafting bananas Stage II
 

Yo, Richard, you must have some script to automatically welcome everyone because you've welcomed Mauro several times now. LOL

Now that I think of, I don't remember ever welcoming you, Richard, so here is your welcome without going back and finding your introductory post. WELCOME!

Now, Mauro, in a more general way, I think you should feel welcome to post your comments about your grafting experiment. You might be crazy, but most of us are crazy one way or another. I find your comments interesting.

Re: Grafting bananas Stage II
 

I hope no one minds me replying to old threads.

It's easier to see in the discrete case. For Richard's example, you're adding up pieces of area under a curve that goes through 1, 1/e, 1/e^2, and so on as x is 0, 1, 2, ... . Instead, add up 1, 1/2, 1/4, and so on. You can see graphically that that adds up to one: cut a square in half; then cut one of the halves in half to get a half and two quarters; then cut one of the quarters in half, to get a half and a quarter and two eighths. And so on.

And then you can see that the shape Richard mentioned has finite area by drawing rectangles along the x axis: one unit high from 0 to 1, half a unit high from 1 to 2, a quarter unit high from 2 to 3, and so on. Leaving out the first, those are the same areas you cut the square into. So they add up to one. Richard's shape is entirely inside the row of rectangles, so it's smaller.