1st Blog - Infinity
What comes to mind when you hear the word infinity? Some might say forever, never ending, or a huge number that makes their head hurt just thinking about it. To me, infinity is so intriguing. I feel like every math course I've taken has had concrete answers to every problem we solve, every concept we engage in and every equation we analyze - except for the idea of infinity. There is nothing concrete about infinity. What really is infinity? Where does it start? Where does it end? Does infinity truly exist?
Aristotle was the first mathematician to give a reasonable description of infinity in terms that are easily understandable to the general population. He divided infinity into two categories - potential infinities and actual infinities. Potential infinities are like numbers. They go on and on forever with no exact ending point. For example, you could count numbers forever and ever, never reaching an end number. This infinity is one that Aristotle confidently believed in. An actual infinity is either numbers or some other mathematical object that come to a final end, as in a set of numbers or the volume of a dense solid. This type of infinity is contained. Unlike potential infinities, Aristotle completely disagreed with actual infinities.
Based on the definitions of these types of infinities, it is hard for me to justify an actual infinity being "infinite". If something is contained and has an ending point - how can it be infinite? Potential infinities do make sense to me with my experiences with infinity. Potential infinities have no concrete end, no finish line. This is what come to my mind when hearing the word infinity. Which infinity do you believe in?
Aristotle was the first mathematician to give a reasonable description of infinity in terms that are easily understandable to the general population. He divided infinity into two categories - potential infinities and actual infinities. Potential infinities are like numbers. They go on and on forever with no exact ending point. For example, you could count numbers forever and ever, never reaching an end number. This infinity is one that Aristotle confidently believed in. An actual infinity is either numbers or some other mathematical object that come to a final end, as in a set of numbers or the volume of a dense solid. This type of infinity is contained. Unlike potential infinities, Aristotle completely disagreed with actual infinities.
Based on the definitions of these types of infinities, it is hard for me to justify an actual infinity being "infinite". If something is contained and has an ending point - how can it be infinite? Potential infinities do make sense to me with my experiences with infinity. Potential infinities have no concrete end, no finish line. This is what come to my mind when hearing the word infinity. Which infinity do you believe in?
It does seem weird to think of actual infinities to be definite, or a contained space. The way I interpret it is like with calculus we find infinitesimally small amounts of area in order to find the overall area. That's how I rationalize that component of actual infinities. I believe in both, but I am definitely more prone to think of potential infinities before actual infinities.
ReplyDeleteHi Jennifer,
ReplyDeleteGreat post! I would definitely agree that at times the idea of infinity can make my head spin in circles. After reading through your post, with my head still spinning, potential infinities also make sense in my head. With that said, I would side with Aristotle because if an actual infinity comes to an, is it an actually an infinity? This post has definitely sparked some questions in my head about infinite numbers and how we categorize them. I'm also interested in the idea of large and small infinities, it's an interesting concept that is starting to make more sense in my head. Overall, great post!! Thanks for sharing your thoughts on this topic.
These posts are evaluated by:
ReplyDeleteClear- if this shows up as an issue, it’s usually about spelling, grammar or structure.
Coherent- has a point and an objective
Complete- looks like 2 hours of work, attends to necessary bits for the point. Sharing your thinking, always a good idea. Cite images or websites you used or referenced.
Content- math and teaching ideas are accurate. (Does not mean no math mistakes. Mistakes are how we get better!)
Consolidated- writing has an end. Synthesize the ideas, pose remaining questions, etc. Sometimes I recommend one or more of: 1) What did I say/do?, 2) Why is it important?, 3) What comes next?
On first writing these are just for feedback. At the end of the semester you pick 3 posts for exemplars. Those can be revised from feedback or just ones you write taking into account the feedback now.
Great topic, and when we cover infinity in class, we'll talk about Aristotle too. The main issue for this post is complete & content, which you could remedy by digging a little deeper. What's happened since Aristotle? What's the history and who are the mathematicians?
C's: 3/5