We add 1 banana to the sequence (=it should change quantitatively and qualitatively).
But is does not change quantitatively(∞+1=∞) or qualitatively(still identical rows of identical bananas). — Devans99
but then there's a difference between each instance of such identicalness by virtue of their inability to occupy the same space at the same time. — TheMadFool
Each banana has a different spatial position I agree, but the two sequences, ignoring their space time position are identical (same mass, same number of bananas, all bananas in one-to-one correspondence). The definition of a sequence (similar to a set) does not include their relative spacial positions - so the two sequences of bananas remain identical whilst they are changed. Which is a contradiction. Hence actual infinity cannot exist. — Devans99
You can't ignore their space-time positions because it's critical to your argument. Why are there infinite bananas? Because they occupy different spaces? If they occupy the same space there would be only one banana. — TheMadFool
Things don't potentially have parts. They actually have parts — Gregory
So we have an infinite bag and we add ten balls and remove one. We repeat that an actually infinite number of time. At each finite step, there are 9n balls in the bag. At actual infinity, there are zero balls in the bag. Reductio ad absurdum, actual infinity is impossible. — Devans99
You need to understand that what the mind thinks geometrically of an object actually applies to it. — Gregory
How many parts does a banana ACTUALLY have? Don't say one because I can split it in half. And if I was all-powerful I could split it up infinitely. Objects are both infinite and finite at the same time. Logic proves this — Gregory
Discreteness does even mean anything. Does the discrete have parts? If not it's zero and has nothing to do with an object — Gregory
But all balls numbered less than ∞ have been removed from the bag at the end of actually infinite steps. So there are zero balls in the bag.
Mathematical induction leads to 9n balls in the bag at each finite step (where n belongs to the natural numbers). You can't use mathematical induction for the infinite part of this problem as it applies for all n belonging to the natural numbers only and ∞ is not a natural number. — Devans99
Then you keep thinking of the division. The numbers of parts go on forever. So infinity does exist — Gregory
Do you potentially have a hand, or do you actually have one? How can something have parts only potentially? How can something exist yet not have parts? These are all non-sensical statements. — Gregory
Just check the math. In the 1st step the 1st ball is removed but there are more than 1 ball. In the 2nd step the 2nd ball is removed but there are more than 2 balls. Ergo at the nth step then nth ball is removed but there are more than n balls. — TheMadFool
Does the discrete part have parts. If it doesn't, why isn't it zero? — Gregory
The world is physical, which is made of infinite parts. If it's more like a simulation, than why are you elsewhere arguing for a God? — Gregory
Are the parts non-zero? Do they have a front and back? Uh, the front and back are parts! This is the paradox started by Zeno. YOU don't have the solution — Gregory
t either has a back and front, or it doesn't. That is, it is either real or zero — Gregory
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