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Suppose a vending machine gives 20 soda for 20$. If someone walks up and inserts 1$ and can get 0 soda, but if they insert an extra 19$ they get 20 soda.

If that’s true then for some amount between 1$ and 20$ inserting an extra 1$ must let you get more than 1 soda in order for it to be handing out 20 soda at 20$.

PS: Back to cancer, if it’s 19 cancer at 20x then you can keep a 1:1 relationship at 2+x and 0 cancer at 1x. Then again if you can’t tell if it’s 19 cancer or 20 cancer then it might just be 21 cancer.




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