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Friend $A$ claims that he has eaten $1$ apple today.

Friend $B$ responds. Congrats, I have eaten $0$ apples, so that is $\infty$ more apples than me.

Friend $C$ says, but I have also eaten $0$ apples. So how many times more than you have I done? $0$ or $\infty$?

Kasper
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    How is friend $B$ correct? Friend $A$ only ate one more apple than friend $B$, not infinitely more. We are only dealing with finite quantities here... – layman Dec 03 '15 at 11:53
  • haha good point @user46944 – Kasper Dec 03 '15 at 11:55
  • What is this, are you trying to say $1/0=\infty$, doesn't make sense to me. – Kushal Bhuyan Dec 03 '15 at 11:55
  • In general, $0\cdot\infty$ is indeterminate, not equal to $1$. The challenge/problem with this type of question is that one cannot treat $\infty$ as a number. I would say that $B$ has eaten $n$ times more apples than $C$ where $n$ is any number. – Michael Burr Dec 03 '15 at 11:55
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    A has eaten infinitely as many apples as B has eaten, in the sense that for any finite number x A has eaten more than x times as many apples as B as eaten. But C has eaten the same amount of apples as B and at the same time 10 times as many apples as B, because 10*0 is 0 obviously. – s.harp Dec 03 '15 at 11:56
  • Its simply all statements: C has eaten x times as many apples as B are true, since both C and B have eaten 0 apples. In the strict sense C has eaten infinitely many times as many apples as B is false, since "infinitely as many" would mean "there is no finite number x so that C has eaten x times as many apples as B". – s.harp Dec 03 '15 at 11:58
  • @user46944 A has not eaten 2 more apples than B. There is a difference between saying I have eaten 2 times as many apples as you and I have eaten 2 more apples than you. – s.harp Dec 03 '15 at 11:59
  • @s.harp OP wrote that friend $B$ said friend $A$ ate infinitely more apples than $B$. – layman Dec 03 '15 at 11:59
  • @user46944 Indeed that is right. I have assumed that to be an error in formulation since otherwise the statements are obviously incorrect. – s.harp Dec 03 '15 at 12:00

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