Cantor on the Shore Category: 9 infinity and beyond

Ethan Haffenden
Fri, 24 Feb 2017 05:49 PM

The blog Cantor by the Shore ( is dedicated to the understanding and appreciation of the mathematical concept of infinity. One of the posts states that the concept of 'To Infinity and Beyond" doesn't make sense seen as infinity goes on forever and there is not a possible way to go past forever. One of the points the blog brings up is Achilles and the tortoise. If the tortoise starts 10 meters before Achilles and then when he reaches where the tortoise was the tortoise is then 1 meter in front of him then they go again and when Achilles is where the tortoise was before it is now 10 centimetres in front of him and so on. This shows that we know Achilles will eventually beat the tortoise however if this pattern is kept up there is no possible way for Achilles to beat the tortoise. The post also discusses the difference between actualist infinity and potential infinity. Actualist interprets the pattern 1/2 + 1/4 + 1/8 and so on as equalling 1, however, potentialist view this pattern as potential 1 because it will never reach one yet if the pattern is continued it will eventually have the ability to reach one. Potentialists currently say that our brains, computers and strategies are just too incompetent to understand the idea of infinity. I believe in the concept of potential infinity and that we currently are incapable of understanding the concept of infinity, hopefully, one day we will be able to understand the concept of infinity.

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