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Is Super-Infinity Larger than Infinity?

Infinity is a pretty common buzzword in both the media and in math. Well in math, it has a pretty important purpose. Infinity is often represented in math courses as a half number, half state that represents some endlessness of the numbers continuum.

To write infinity on Parsegon, you simply write: "infinity". A common case is an integral from 2 to infinity or something of that sort. But it is worth noting that the conversation of infinity does not stop at infinity. There is a whole branch of thinking dedicated to this single issue.

If you haven't seen V Sauce's rant on the thinking process behind infinity, I highly recommend it. You can access it here on Youtube. The idea is that infinity can have infinity's technically larger than some other infinity's. For instance, take the power set of all sets in the numberline between 0 and infinity. That set constantly grows exponentially faster than a "normal" infinity grows. With every number in infinity, you cannot match it 1 to 1 with the power set infinity.

The point of this blog post isn't meant to be a long history of this study, but it is worthwhile topic to think about. While the V Sauce video does explain it best, do read into what alef naught means and how the line of alefs help us categorize the relative size of infinity. In my opinion, wikipedia does a pretty good job here.

As for now, if you ever need to represent alef naught on Parsegon, just type: "alef naught" - simple as usual :). Of course, aleph, the alternate spelling, also works, as does alef-zero, alef-null, etc. etc you name it.

Photocredits to Vivian Shen.