Infinity: Adam Ibrahim Section 6637

It could be anything.

I chose this picture because I feel that it very perfectly represents infinity. I or anyone here can give me a vague description of what it is—you can tell me the dimensions of the photo itself, and you can tell me the color that you can see in it (which is, of course, white) but otherwise, the picture utterly lacks a definable identity. It may very well be blank, or it may very well contain any geometric structure with indefinite dimensions that span indefinite magnitudes, and we can’t see it at all. This picture is exactly what we want it to be when we need it to be for any argument of our choosing. This is exactly what I find infinity to be. It spans over a magnitude that is simply indefinite and functions in a manner of our choosing, so long as we stick to the concept that it is bigger than any finite number. (Haha Mr. Reitz! A smartass to the end! To the bitter end!)

I can’t remember the first time I was exposed to the idea of infinity. I do remember not being very shocked, amazed or perturbed by the idea in any way. Something about it just seemed… right. The first example I can remember was in seeing who could think of the biggest number. One kid said infinity. Someone else quickly jabbed back with, “Oh yeah? Well how about infinity plus infinity?” Which led right into, “Pfft, infinity times infinity.” Then I chimed in with, “What about infinity raised to the infinity power?” Since no one could beat that method, the argument was pretty much decided by who could repeat “to the infinity” the more times than everyone else.

The first time I ever really ran into trying to define infinity was when learning about how numbers are defined in a hierarchy, starting with counting numbers and ending in complex numbers. Since each larger set included the last, I figured one could conclude that each set was larger than the last, even though each set included an infinite amount of numbers. In order to probe the subject, I asked my teacher this question: “If the set of counting numbers includes an infinite amount of numbers, then does the set of whole numbers include infinity plus 1, since the only new inclusion in that set is 0?” To this, my teacher responded no, and I was pretty confused. I didn’t really see why it shouldn’t be defined that way. I figured that it could work something like this:

Counting Numbers: This set is infinite by itself.

Whole Numbers: There is an addition of 0 to this set, one extra entry.

Integers: For each Counting number, there is now a polar opposite.

Rational Numbers: For each integer, there is an infinite set of numbers in between, for each entry of an infinite set there is an infinite set.

I knew that the definition was indefinite and abstract, and it didn’t have to yield any real tangible result, but it irked me that it didn’t work. Infinity started to bother me when I started to realize that its definition was more elusive than I was led to believe.