Infinity: Are We There Yet?
Jason Harrington
Infinity: when most people hear this word, they think of something large or
something vast. Some people think of space or time, while others think of life after death.
Mathematicians are faced with this concept almost everyday. Yet, what does it really
mean? Is it practical to even think about infinity? What did the early civilizations think
about infinity? How has our thinking of infinity changed overtime?
To start off, a mental experiment needs to be done to see how complex infinity
can be. Let’s say there are two bags that hold numbers. In both bags, we place the first 10
numbers starting from 1 to 10. In the first bag, we remove the smallest number, 1. In the
second bag, we remove the largest number, 10. Then we put in the next 10 numbers in
both bags from 10 to 20. Again, in the first bag, we remove the smallest number, in this
case, 2. In the second bag, we remove the largest number, which is the number 20. Now
we repeat again. Both bags have the same number of items in them along each step, since
we always put in 10 items and remove one. However, in the first bag, every number will
eventually be removed since the smallest is removed each time, while in the second bag
there are infinitely many numbers that will never be removed, such as 2. So even though
both bags have the same number of items along each step, the way we remove an item
affects what happens as we do this process an infinite number of times. The first bag will
be empty after we do this process an infinite number of times, while the second bag will
become infinitely large. So infinity cannot be thought of simply as a large number as most
people tend to think. So there must be something else to infinity, something that
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