From Netflix’s “The Story of Maths” series, Georg Cantor was introduced to me, and from Google’s search I landed on Numberphile’s “Infinity is bigger than you think” YouTube video. I totally understand the logic in which Georg Cantor wanted the world to know that infinity does have different sizes, but the logic within me just steers me away from Cantor’s infinities altogether.
If you watch the YouTube video I’d mentioned (don’t worry… I’ll post it at the bottom of this post), you should understand why Cantor’s diagonal argument depicts that infinity does come in different sizes. Basically, the idea of infinity with different sizes is very well explained in the YouTube video that I’d mentioned of. Nonetheless, what is bothering me is that numbers exist only in our mind, and they have nothing to do with infinity. Furthermore, infinity is a concept in which could both be true and imaginary.
Whenever a whole number infinity size is being measured to so called larger decimal infinity size, within me would logically beg the differ for I see that each decimal number is just a representation of each whole number. Thus, in Cantor’s diagonal argument, I imagine that there is only one infinity in which you can draw however different sizes of infinity within one true infinity. In a way, I don’t see Cantor is being wrong, but I’m seeing that there must always be that one more infinity which can hold all other infinities within. In a sense, these so called different infinities should be one of the same, because they’re all connected (interconnected) together.
Anyhow, check out the YouTube video I’d mentioned earlier right after this break. Enjoy!