Consider this odd situation. At my feet are an Infinite number of baseballs numbered 1,2,3 and so on. In front of me is a door that leads into an infinitely large room. At exactly eight minutes to midnight, I throw balls 1 and 2 into the room. Immediately someone in the room throws ball 1 back out. At four minutes to midnight (half of eight minutes), I throw balls 3 and 4 into the room. Immediately someone in the room throws ball 2 back out. At two minutes to midnight (half of four minutes), I throw the next 2 balls,5 and 6, into the room, and Immediately ball three is thrown back out.
At one Minute, half a minute, a quarter a minute and so on, I throw the next two balls into the room, and Immediately one ball is thrown back out. Of course this presumes that I can keep throwing balls faster and faster in shorter amounts of time.
At exactly midnight, how many balls are in the room? Which of thses do you belive to be true and why?

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  1. An Infinite number
  2. Half of Infinity
  3. Zero
  4. None of the Above

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First off, you can't have half of infinity. Infinty is not a number, and therefore cannot have a half. Infinity divided by 2 is still infinity.

I say the answer is infinity. Why, because it seems so. Might be zero as well. But who is to say it is some number that we haven't discovered yet?

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Zero. As soon as you break the speed of light, you will traverse back in time, and undo your own throwing.

Or, if you want to hold yourself to your silly little Zeno paradox, infinity.

Mr U

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Iam going to go with infinity because infinity is an endless amount of something and there for it can not be put in half.

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Well, according Zeno, who as I have previously stated I believe is full of shit, the answer will be none of the above, since according to him midnight will never arrive. That is probably the best proof to show he is full of shit actually. Reaching midnight is like reaching the end of the running track... doesn't happen apparantely only it does.

According to logic and common sense, midnight will arrive, but you will never stop throwing, which makes no sense whatsoever.
So the answer is still none of the above
There is no possible solution because the given facts about the situation contradict themselves. It's a faulty equation. You can't throw an infinite amount of balls an infinite amount of times in a set time...

HU, I don't know how you get the going back in time thing. The way I see it, when you pass the speed of light you will simply throw the balls too fast for the eyes to see, and it'll be like watching a recorded video.....

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Zero: Every ball thrown in is eventually thrown out before midnight, so no balls remain

Half of Infinity: Each time I throw balls into the room, the person inside the room throws half of Infinity back out , leaving half of Infinity inside (Of course half of Infinity is still Infinity)

None Of the Above: The question itself is flawed because there is a limit to the speed at which balls can be thrown. And if you keep halfing the time Miodnight would never reach.

This was a question in my previous physics class or was it calculus anyway, we had to provide an awnser on how each could be true.

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I would go with none of the above......but you already explained why....

Still sour at old Zeno, eh? Lol.

Here's a question: Is 0/0 an indeterminable number, or is it in fact equal to every fraction?

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0/0 Is nothing at all. It cant be equal to every fraction if there is "nothing" to be equal with.

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Ah, but there is at least some logic behind saying that it is equal to all fractions. The chart below is an array of fractions. The lines extending across the chart intersect with familiar fractions that are equal of value, and all lines coincide at 0/0. With the lines connecting equal values of all fractions, it appears 0/0 is equal to every fraction.

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Argh, stupid attachment.

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