Are These Containers
Full or Empty?

An Experimental Investigation of Infinity Utilizing
the Scientific Method

Problem

Are the containers full or empty?

Hypothesis

First Container: Full Second Container: Full

Experiment Procedures

First, we cut about 100 small squares of paper and makes two piles of 50 pieces. We labeled each set 1-50. Next we found some container that we could use to put the pieces of paper in. From our first set of 50 numbers, we put in the pieces labeled 1-10 and drew out the number 1. We continued with the process until all 50 pieces were in and the numbers 1-5 were drawn as stated in the directions to the first container. The process was repeated for the second container except this time we drew out the multiples of 10.

Students may include drawings here to illustrate.

Revised Hypothesis

We still think that both containers are full.

Conclusion

We were right about the second container but the first container was tricky. It seemed that there would still be some numbers left if you stopped at some point.

So, the first container is empty because we can not name a number that would be left, and the second is full because there are many numbers that we could name that would be left. It is pretty cool that probability can be used as a tool to prove ideas about infinity.

Are the containers full or empty?

Hypothesis

First Container: Full Second Container: Full

Experiment Procedures

First, we cut about 100 small squares of paper and makes two piles of 50 pieces. We labeled each set 1-50. Next we found some container that we could use to put the pieces of paper in. From our first set of 50 numbers, we put in the pieces labeled 1-10 and drew out the number 1. We continued with the process until all 50 pieces were in and the numbers 1-5 were drawn as stated in the directions to the first container. The process was repeated for the second container except this time we drew out the multiples of 10.

Students may include drawings here to illustrate.

Revised Hypothesis

We still think that both containers are full.

Conclusion

We were right about the second container but the first container was tricky. It seemed that there would still be some numbers left if you stopped at some point.

So, the first container is empty because we can not name a number that would be left, and the second is full because there are many numbers that we could name that would be left. It is pretty cool that probability can be used as a tool to prove ideas about infinity.